This cookie is set by GDPR Cookie Consent plugin. going to be our change in X. I just wrote the Greek How do you find the component form of the resultant vector? Posted 7 years ago. Direct link to zsoltturi's post I wonder how to calcualte, Posted 4 years ago. Therefore, you can say that. WebThe resulting vector formula can be used in physics, engineering and mathematics. Take the square root of the previous result, and this is the magnitude of your two vectors' sum! There are a two different ways to calculate the resultant vector. And I'm ending up at Y is equal to, let me do that in that other color. Adding vectors A + B + C gives the same resultant as adding vectors B + A + C or even C + B + A. The resultant vector is the vector that results from adding two or more vectors together. Problem 1.1 \vec u = (1,7) u = (1,7) The component form of the resultant vector 2u - 3v = (33,10) The answer is 33 on the y-axis and 10 on the x-axis.. What is a vector? i.e given a vector V(p, q), the magnitude of the vector is given by |V| = sqrt(p^2 + q^2).#trigonometry#vectors#vectors There are a two different ways to calculate the resultant vector. Shouldn't the vector be -11,-12 instead of (-11,-12)? Having a good knowledge of vector operations is important as in physics we have to deal with numerous vector quantities. These components are then used to find the resultant vectors magnitude and direction, which is AB. 1) or where you end up, so that's negative seven, and you subtract your WebComponents of a Vector Definition. The vector V is broken into two components such as v x and v y. This website uses cookies to improve your experience while you navigate through the website. Solving Cubic Equations - Methods and Examples. Let vector lltll= 44mph with a direction of 240 Let vector b have a magnitude of 32 mph at a direction of 100 . The three resultant vector formulas are: R = A + B. R = A - B. R2 = A2 + B2 + 2ABCos . Q: Write the component form of a vector v with initial point P and terminal point Q. P (-1,-10), Q (-1,. WebAnswer to Solved Find the component form of the resultant vector. If one-third of one-fourth of a number is 15, then what is the three-tenth of that number? I think i missed something along the way. How do you find the resultant vector in component form? Q: Write the component form of a vector v with initial point P and terminal point Q. P (-1,-10), Q (-1,. In this case, the direction is left and down. We use cookies on our website to give you the most relevant experience by remembering your preferences and repeat visits. The resultant vector formula for the given vectors is given by- r = a + b = (i+2j+3k) + (4i+8j+12k) = 5i+10j+15k The resultant vector from the given vectors is 5i+10j+15k Question 2: Find the resultant vector for the vectors i-2j+5k and 2i-4j+10k Solution: Given two vectors are a=i-2j+5k and b=2i-4j+10k Let a and b are the vectors with the same direction then the resultant vector r is given by-, If the vectors are in different directions then the resultant of the vector can be calculated by subtracting the vectors from each other. Draw a vector diagram to find the resultant of each pair of vectors using the triangle method. WebTranscribed Image Text: Find the component form of the resultant vector. WebGiven a vectors initial point (where it starts), (x, y), and terminal point (where it ends), (x, y) the component form can be found by subtracting the coordinates of each point: < x x, y y > Learn what it means to bring Yup to your school or district Schedule Demo And then, the second direction. So our change in Y, our change in Y, what's WebVector Calculator. WebAnswer to Solved Find the component form of the resultant vector. The cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional". How do I find which quadrant the vector would be in? Is paralegal higher than legal assistant? Cross product of two vectors (vector product), Online calculator. What is the pedagogical reason for using parenthesis vector notation? From there you find your change in x and change in y through subtraction or construction of your own graph. Question: Give the component form of the resultant vector in the following. The vector V is broken into two components such as v x and v y. To move to the left on the x-axis and down on the y-axis would be to move down in numbers, thus negative. Can you determine the mathematic question in this equation? Here a2, b2 represents magnitude of the vector a, b. The resultant vector formula for the given vectors is given by-, The resultant vector from the given vectors is 5i+10j+15k, Question 2: Find the resultant vector for the vectors i-2j+5k and 2i-4j+10k, Given two vectors are a=i-2j+5k and b=2i-4j+10k, The resultant vector from the given vectors is 3i-6j+15k, Question 3: Find the resultant vector for the vectors 2i-2j+k and 2i+7j+3k, Given two vectors are a=2i-2j+k and b=2i+7j+3k. Direct link to Aleks Jevtic's post What about 3 Dimensional , Posted 3 years ago. This website uses cookies to improve your experience while you navigate through the website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. We provide quick and easy solutions to all your homework problems. "So I have to go to the left 11 spaces." tan = Ax Ay tan = A x A y. or, = tan1(Ax Ay) = tan 1 ( A x A y) This is how you identify the direction angle of a vector in a plane when you have knowledge of x and y components of a vector. WebLearn how to write a vector in component form given two points and also how to determine the magnitude of a vector given in component form. The angle labeled as theta () is the angle between the resultant vector and the west axis. The head to tail method is way to find the resultant vector. A: The length of a vector x=abc is given by the equation; ||x||=a2+b2+c2. Two-dimensional vectors. 14. The thing is you subtract ENDING POINT - STARTING POINT. The head to tail method is way to find the resultant vector. These cookies help provide information on metrics the number of visitors, bounce rate, traffic source, etc. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. There are a two different ways to calculate the resultant vector. The interaction of several force vectors on a body is an example of the resultant vector, and the resulting vector is obtained using this formula. Sometimes we are only interested in the magnitude or size of the resultant vector. WebHow do we use the components of two vectors to find the resultant vector by adding the two vectors ? This cookie is set by GDPR Cookie Consent plugin. Table of Content. Components of a Vector. WebGiven a vectors initial point (where it starts), (x, y), and terminal point (where it ends), (x, y) the component form can be found by subtracting the coordinates of each point: < x x, y y > Learn what it means to bring Yup to your school or district Schedule Demo WebThese two components are supposed to form a right-angled triangle. Analytical cookies are used to understand how visitors interact with the website. 14. The values a, b, c are called the scalar components of vector A, and a ^i i ^, b ^j j ^, c ^k k ^, are called the vector components. The interaction of several force vectors on a body is an example of the resultant vector, and the resulting vector is obtained using this formula. It does not store any personal data. WebIn each direction, use this format: F = (Force) + (Force) + (Force). The y component of the balls velocity vector is vy. Area of triangle formed by vectors, Online calculator. Let a, and b are two vectors inclined to each other at an angle , then the resultant vector r is given by-. ( 2 votes) khalid 5 years ago why we call the the change in x and the change in y component of the vector ? Are there situations in which components are preferable to unit vectors (i-hats and j-hats) and vice versa? The head to tail method is way to find the resultant vector. Does that help? if I'm going from four "to negative seven, I have to go down four "just to get back to X equals zero, "and then I have to go down another seven. Component form of a vector with initial point and terminal point This free online calculator help you to find vector components (vector coordinates) through two points (initial and terminal points) very simply. WebExplanation: . Suppose a vector V is defined in a two-dimensional plane. Direct link to loumast17's post Vector addition, or subtr, Posted 6 years ago. If displacement vectors A, B, and C are added together, the result will be vector R. As shown in the diagram, vector R can be determined by the use of an accurately drawn, scaled, vector addition diagram. To find the resultant of two vectors in component form, just add the x components of each and the y components of each. How do you find the resultant vector in component form? As long as all three vectors are included with their specified magnitude and direction, the resultant will be the same. The angle labeled as theta () is the angle between the resultant vector and the west axis. Welcome to OnlineMSchool. A force of 5 N acts to the right, and a force of 3 N act to the left. Component form of a vector with initial point and terminal point in space, Exercises. What is the probability sample space of tossing 4 coins? WebComponent form of a vector Mathematics High School answered Find the component form of the resultant vector.1) u = (20,-21) find -3u jazestab is waiting for your help. WebVector Addition. And why. where x is the magnitude of vector x and y is the magnitude of vector y. Q: Write the component form of a vector v with initial point P and terminal point Q. P (-1,-10), Q (-1,. initial point, minus four, which is going to be equal to negative 11. WebComponent form of a vector Mathematics High School answered Find the component form of the resultant vector.1) u = (20,-21) find -3u jazestab is waiting for your help. The angle labeled as theta () is the angle between the resultant vector and the west axis. WebYou'll get a detailed solution from a subject matter expert that helps you learn core concepts. WebTo find the resultant of two vectors in component form, just add the x components of each and the y components of each. So that right over there A vector has both magnitude (which is its length) and direction (which is its angle). Step 1: Line up the head of the first vector with the tail of the second vector, which is automatic for this problem. Who does the voice of Vanessa on Phineas and Ferb? By Checking the Value of "a" and "b" in the Vector we can Understand the Quadrant of the VectorSince the Values of (a,b) are Co-ordinates in the Co-ordinate Plane. Add your answer and earn 378 Tutors 9 Years on market 74934+ Completed orders Get Homework Help WebThis physics video tutorial explains how to find the resultant of two vectors. WebTo find the magnitude of a vector from its components, we take the square root of the sum of the components' squares (this is a direct result of the Pythagorean theorem): || (a,b)||=\sqrt {a^2+b^2} (a,b) = a2 + b2 For example, the magnitude of (3,4) (3,4) is \sqrt {3^2+4^2}=\sqrt {25}=5 32 +42 = 25 = 5. The component form of vector AB with A(Ax, Ay) and B(Bx, By) can be found using the following formula: Three-dimensional vectors. What is the resultant of 3 vectors? If you're seeing this message, it means we're having trouble loading external resources on our website. Learn about Vectors and Dot Products. What is the resultant of 3 vectors? then finding the direction is taking the inverse tangent of the ratio of the combined j steps over the combined i steps. Direct link to Jordan Cooper's post Are there situations in w, Vector components from magnitude and direction. tan = Ax Ay tan = A x A y. or, = tan1(Ax Ay) = tan 1 ( A x A y) This is how you identify the direction angle of a vector in a plane when you have knowledge of x and y components of a vector. In mathematics, we often heard about the two terms scalar and vector. This physics video tutorial explains how to find the resultant of two vectors.Access The Full 31 Minute Video on Patreon:https://www.patreon.com/MathScienceTutorDirect Link to The Full Video on Patreon:https://bit.ly/3ifmoreList of Physics Videos on Patreon:https://www.youtube.com/watch?v=UpYNqI_gh-wPhysics Final Exam - 6 Hour Review - 100 Practice Problems:https://bit.ly/3QetDwgFull 31 Minute Video on Youtube:https://www.youtube.com/watch?v=IoborUarjm4Join The Youtube Membership Program:https://www.youtube.com/channel/UCEWpbFLzoYGPfuWUMFPSaoA/join Distance Formula & Section Formula - Three-dimensional Geometry, Arctan Formula - Definition, Formula, Sample Problems, Class 12 RD Sharma Solutions - Chapter 25 Vector or Cross Product - Exercise 25.1 | Set 3. Given a vectors initial point (where it starts), (x, y), and terminal point (where it ends), (x, y) the component form can be found by subtracting the coordinates of each point: < x x, y y >. WebThe component form of a vector is given as x, y , where x describes how far right or left a vector is going and y describes how far up or down a vector Fast answers In a world where we can get answers to our questions faster than ever before, it's important to have a source that can give us the information we need quickly and accurately. How would I calculate and express the angle it builds with the planes of the origin? However, you may visit "Cookie Settings" to provide a controlled consent. 1 Component form = 1 1, 3 ( 3) (x. Draw a vector diagram to find the resultant of each pair of vectors using the triangle method. count the squares, you could say, "Look, ( 2 votes) khalid 5 years ago why we call the the change in x and the change in y component of the vector ? These cookies track visitors across websites and collect information to provide customized ads. Direct link to Wild Chaser's post In quadrant 4 why are we , Posted 6 years ago. WebThe procedure to use the resultant vector calculator is as follows: Step 1: Enter the vectors in the respective input field Step 2: Now click the button Calculate Resultant Vectors to get the result Step 3: Finally, the resultant vector will be displayed in the output field What is Meant by the Resultant Vectors? Step 1: Line up the head of the first vector with the tail of the second vector, which is automatic for this problem. Find: First, find both vectors from the initial and final points: Now find the sum of both vector by adding the components separately: Web/ 4ind a vector in component form that has a direction of256 and a magnitude of 12 ft. <12.CD 25 , 1.2 sin 5"") (-2. qo 3J -II. Direct link to zzzwhking's post problem2.2 has two answer, Posted 6 years ago. We also use third-party cookies that help us analyze and understand how you use this website. How to find the vector component in the Y-axis? The angle labeled as theta () is the angle between the resultant vector and the west axis. The cookie is used to store the user consent for the cookies in the category "Performance". The y component of the balls velocity vector is vy. "We started at negative four." By using our site, you WebThe resulting vector formula can be used in physics, engineering and mathematics. So, this point right over here, point A, its coordinates are (4,4). This method involves properties of parallelograms but, in the end, boils down to a simple formula. when sal sir says "negative 4" why he denotes to "positive 4"? By clicking Accept All, you consent to the use of ALL the cookies. In the graph above x1=0, y1=0 and x2=2, y2=5. The ordered pair that describes the changes is (x2- x1, y2- y1), in our example (2-0, 5-0) or (2,5). WebThe component form of a vector is given as x, y , where x describes how far right or left a vector is going and y describes how far up or down a vector Fast answers In a world where we can get answers to our questions faster than ever before, it's important to have a source that can give us the information we need quickly and accurately. That is, the net force is the resultant of all the forces; it is the result of adding all the forces together as vectors. Find: First, find both vectors from the initial and final points: Now find the sum of both vector by adding the components separately: To find the resultant of two vectors in component form just add the x components of each and the y components of each. Direct link to Nataly Barrios Garcia's post How do you know what dire, Posted 3 years ago. How many times should a shock absorber bounce? Example 2: Find the resultant of the vectors having magnitudes of 5 units, 6 units, and are inclined to each other at an angle of 60 degrees. purely in the Y direction. WebThe following resultant vector formula can be used here. Yep, you use the components and trigonometry to determine the angle of the vector, and that tells you the direction. WebExplanation: . If you want to contact me, probably have some question write me email on support@onlinemschool.com. The resultant vector from the given vectors is 17.31. Given two vectors are a=2i+2j+2k and b=i+2j+3k, Also given that given two vectors are inclined at an angle =30, So the resultant vector formula for the given vectors is given by-, Magnitude of vector a (a2) = \sqrt{2^2+2^2+2^2}, Magnitude of vector b (b2) = \sqrt{1^2+2^2+3^2}, The resultant vector from the given vectors is 29.65. Web/ 4ind a vector in component form that has a direction of256 and a magnitude of 12 ft. <12.CD 25 , 1.2 sin 5"") (-2. qo 3J -II. Vectors Algebra Index. Why did he start from A (4,4) instead of B (-7,-8). Why is having a good knowledge of vector operations important? Functional cookies help to perform certain functionalities like sharing the content of the website on social media platforms, collect feedbacks, and other third-party features. Table of Content. Scalar is a quantity which has only magnitude i.e. Scalar-vector multiplication, Online calculator. This technique can be applied to both graphical and algebraic methods of In the picture on the left, the black vector is the resultant of the two red vectors. Can you solve for a resultant force given its components? If you roll a dice six times, what is the probability of rolling a number six? Direct link to loumast17's post If you have all three coo, Posted 3 years ago. ; The head to tail method is way to find the resultant vector. Sometimes all you need is a fresh perspective to see the answer. WebFind the component form of the resultant vector - When you try to Find the component form of the resultant vector, there are often multiple ways to approach it. You ALWAYS subtract the points. WebIn each direction, use this format: F = (Force) + (Force) + (Force). Scalar quantity describes the distance. When you try to Find the component form of the resultant vector, there are often multiple ways to approach it. Two vectors are equal if they have the same magnitude and direction. Luis Hoyos. The head to tail method is way to find the resultant vector. Addition and subtraction of two vectors on plane, Exercises. WebAs we know that the resultant vector is given as: R = OA + OB +OC R = 5 + 10 + 15 R = 30N Example 2 Find out the resultant vector of the given Get help from expert tutors If you're struggling with a particular subject, get help from one of our expert tutors. Q: Find the length of the vector a %3D. How do you calculate working capital for a construction company? WebHow to Find the Components of a Vector? Direct link to Tolbert Jena''s post Why did he start from A (, Posted 7 years ago. WebThe parallelogram method to calculate resultant vector. To find out how fast the ball is traveling toward the table edge, you need not the balls total speed but the x component of the balls velocity. You can always count on us for help, 24 hours a day, 7 days a week. Direct link to william_hinkley's post What is the pedagogical r, Posted 5 years ago. Add your answer and earn 378 Tutors 9 Years on market 74934+ Completed orders Get Homework Help Now complete the summing to calculate the net force in each direction. Components of a Vector. WebFinding a resultant vector using components of a vector is known as an analytical method; this method is more mathematical than geometrical and can be regarded as more accurate and precise than the geometrical method, A vector has both magnitude (which is its length) and direction (which is its angle). A vector is an object that has both a magnitude as wel as direction. WebThe following resultant vector formula can be used here. You can navigate between the input fields by pressing the keys "left" and "right" on the keyboard. What is the resultant of 3 vectors? To find the resultant of two vectors in component form, just add the x components of each and the y components of each. Two vectors are shown below: #color(red)(vec(OA) and vec(OB)# We will also be using these vectors in our example later. Component form of a vector with initial point and terminal point This free online calculator help you to find vector components (vector coordinates) through two points (initial and terminal points) very simply. WebVector Calculator. These cookies will be stored in your browser only with your consent. The vector component in the y-axis, is approximately 22.6. Component form of a vector with initial point and terminal point, Online calculator. Direct link to Mr. Ott's post Remember, in a vector, th, Posted 7 years ago. To find out how fast the ball is traveling toward the table edge, you need not the balls total speed but the x component of the balls velocity. This cookie is set by GDPR Cookie Consent plugin. It may be to underline the fact that there really is no difference between a vector and a standard ordered pair. Question 5: Find the resultant of the vectors 2i+2j+2k and i+2j+3k which are inclined at an angle 30 to each other. And then how much do we have In the picture on the left, the black vector is the resultant of the two red vectors. This cookie is set by GDPR Cookie Consent plugin. The component form of a vector is the ordered pair that describes the changes in the x- and y-values. What are the benefits of board and batten siding? If you're looking for help with your homework, our team of experts have you covered. WebThe component form of a vector is given as x, y , where x describes how far right or left a vector is going and y describes how far up or down a vector Fast answers In a world where we can get answers to our questions faster than ever before, it's important to have a source that can give us the information we need quickly and accurately. These cookies ensure basic functionalities and security features of the website, anonymously. How to convert a whole number into a decimal? WebFinding a resultant vector using components of a vector is known as an analytical method; this method is more mathematical than geometrical and can be regarded as more accurate and precise than the geometrical method, Plus, every point on a graph can be described as the terminal end of a position vector, so an ordered pair can be thought of as the end of a vector. But opting out of some of these cookies may affect your browsing experience. When it comes to solving vector components, I am still confused when to add or subtract the points. WebLearn how to write a vector in component form given two points and also how to determine the magnitude of a vector given in component form. Add your answer and earn 378 Tutors 9 Years on market 74934+ Completed orders Get Homework Help WebFind the component form of the resultant vector - When you try to Find the component form of the resultant vector, there are often multiple ways to approach it. It does not store any personal data. So two vectors are in opposite direction. Methods for calculating a Resultant Vector: The head to tail The ordered pair that describes the changes is (x2- x1, y2- y1), in our example (2-0, 5-0) or (2,5). Enter values into Magnitude and Angle or X and Y. Invest in math tutoring to support student remediation and acceleration. Then state the magnitude and direction angle of the resultant. Using this online calculator, you will receive a detailed solution to your problem, which will help you understand the algorithm solving to determine the coordinates of vector and to fix the passed material. If you were to add this red WebComponent form of a vector with initial point and terminal point Online calculator. 1) u = (-11, 2) b= (10,-4) 2) u = (6, 11) b = (1, -10) Find:-u- Find: -u + b 3) f= (12, 12) = (6, -12) Find: -f+ Remember, in a vector, there is a specific beginning and ending point, and the ending point is marked as an arrow. Consider a vector v. Its two components directed along the x and y-axis would be vx and vy, respectively. Resultant vector formula gives the resultant value of two or more vectors. The head to tail method is way to find the resultant vector. Components of a Vector. In the graph above x1=0, y1=0 and x2=2, y2=5. Wouldn't the change in x and y be ( 11, 12 ) ? More in-depth information read at these rules. Two vectors are equal if they have the same magnitude and direction. The vector A A in the below image is called the component form. Necessary cookies are absolutely essential for the website to function properly. If vector A = 12i 16j and vector B = 24i + 10j, what is the direction of the vector C = 2A B? WebFind the component form of the resultant vector. Dot product of two vectors in space, Exercises. Learn how. Write the component form and find the direction of the resultant. But opting out of some of these cookies may affect your browsing experience. The cookie is set by the GDPR Cookie Consent plugin and is used to store whether or not user has consented to the use of cookies. So, if the direction defined by the problem is "A to B", you subtract Point B - Point A. WebThe procedure to use the resultant vector calculator is as follows: Step 1: Enter the vectors in the respective input field Step 2: Now click the button Calculate Resultant Vectors to get the result Step 3: Finally, the resultant vector will be displayed in the output field What is Meant by the Resultant Vectors? WebGiven a vectors initial point (where it starts), (x, y), and terminal point (where it ends), (x, y) the component form can be found by subtracting the coordinates of each point: < x x, y y > Learn what it means to bring Yup to your school or district Schedule Demo WebHow to Find the Components of a Vector? Direct link to jwinder47's post I think there's only one , Posted 5 years ago. Therefore, we have. WebComponent form of a vector with initial point and terminal point Online calculator. How do you find the component form of a resultant vector? The values a, b, c are called the scalar components of vector A, and a ^i i ^, b ^j j ^, c ^k k ^, are called the vector components. left parenthesis, a, comma, b, right parenthesis, vertical bar, vertical bar, left parenthesis, a, comma, b, right parenthesis, vertical bar, vertical bar, equals, square root of, a, squared, plus, b, squared, end square root, theta, equals, tangent, start superscript, minus, 1, end superscript, left parenthesis, start fraction, b, divided by, a, end fraction, right parenthesis, tangent, start superscript, minus, 1, end superscript, left parenthesis, start fraction, b, divided by, a, end fraction, right parenthesis, tangent, start superscript, minus, 1, end superscript, left parenthesis, start fraction, b, divided by, a, end fraction, right parenthesis, plus, 180, degree, tangent, start superscript, minus, 1, end superscript, left parenthesis, start fraction, b, divided by, a, end fraction, right parenthesis, plus, 360, degree, vertical bar, vertical bar, u, with, vector, on top, vertical bar, vertical bar, left parenthesis, vertical bar, vertical bar, u, with, vector, on top, vertical bar, vertical bar, cosine, left parenthesis, theta, right parenthesis, comma, vertical bar, vertical bar, u, with, vector, on top, vertical bar, vertical bar, sine, left parenthesis, theta, right parenthesis, right parenthesis, left parenthesis, 3, comma, 4, right parenthesis, start color #11accd, start text, m, a, g, n, i, t, u, d, e, end text, end color #11accd, start color #1fab54, start text, d, i, r, e, c, t, i, o, n, end text, end color #1fab54, vertical bar, vertical bar, v, with, vector, on top, vertical bar, vertical bar, square root of, 3, squared, plus, 4, squared, end square root, equals, square root of, 25, end square root, equals, 5, u, with, vector, on top, equals, left parenthesis, 1, comma, 7, right parenthesis, vertical bar, vertical bar, u, with, vector, on top, vertical bar, vertical bar, equals, tangent, start superscript, minus, 1, end superscript, left parenthesis, start fraction, 4, divided by, 3, end fraction, right parenthesis, approximately equals, 53, degrees, left parenthesis, 3, comma, minus, 4, right parenthesis, tangent, start superscript, minus, 1, end superscript, left parenthesis, start fraction, minus, 4, divided by, 3, end fraction, right parenthesis, approximately equals, minus, 53, degrees, minus, 53, degrees, plus, 360, degrees, equals, 307, degrees, left parenthesis, minus, 3, comma, 4, right parenthesis, tangent, start superscript, minus, 1, end superscript, left parenthesis, start fraction, 4, divided by, minus, 3, end fraction, right parenthesis, approximately equals, minus, 53, degrees, minus, 53, degrees, plus, 180, degrees, equals, 127, degrees, u, with, vector, on top, equals, left parenthesis, 5, comma, 8, right parenthesis, 2, slash, 3, space, start text, p, i, end text, u, with, vector, on top, equals, left parenthesis, vertical bar, vertical bar, u, with, vector, on top, vertical bar, vertical bar, cosine, left parenthesis, theta, right parenthesis, comma, vertical bar, vertical bar, u, with, vector, on top, vertical bar, vertical bar, sine, left parenthesis, theta, right parenthesis, right parenthesis, start color #11accd, 2, end color #11accd, start color #1fab54, 30, degrees, end color #1fab54, left parenthesis, start color #11accd, 2, end color #11accd, cosine, left parenthesis, start color #1fab54, 30, degrees, end color #1fab54, right parenthesis, comma, start color #11accd, 2, end color #11accd, sine, left parenthesis, start color #1fab54, 30, degrees, end color #1fab54, right parenthesis, right parenthesis, equals, left parenthesis, square root of, 3, end square root, comma, 1, right parenthesis, u, with, vector, on top, approximately equals, left parenthesis, space, I think there's only one answer that fits the question.
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