Explanation Procedure used: To find x and y components of a vector: 1. Place the vector A such that θ is in standard position. 2. Calculate A x and A y from A x = A cos θ and A y = A sin θ . Use the reference angle if the direction of the component is noted. 3. Check the components to see if each is in the correct direction and has a magnitude that is proper for the reference angle. Adding vectors by components: 1. Add the x -component of the given vectors to obtain R x . 2. Add the y -component of the given vectors to obtain R y . 3. Find the magnitude of the resultant R . Use the equation R = R x 2 + R y 2 . 4. Find the standard-position angle θ for the resultant R . Find the reference angle θ r e f for the resultant R by using the equation θ r e f = tan − 1 | R y | | R x | . Then, use the reference angle and the quadrant of R to determine the standard position angle θ . Calculation: The given vectors, A = 18 is directed at an angle θ A = 0.0 ° and B = 12.0 is directed at an angle θ B = 27.0 ° Sketch the figure of the corresponding vectors as shown below in Figure 1. From Figure 1, it is observed that the resultant vector is represented as R . The x and y components of the vector A are, A x = A cos θ and A y = A sin θ A x = 18 cos 0 ° and A y = 18 sin 0 ° A x = 18 and A y = 0 Similarly, the x and y components of the vector B are, B x = B cos θ and B y = B sin θ B x = 12 cos 27 ° and B y = 12 sin 27 ° B x ≈ 10.69 and B y ≈ 5.45 Then, the x component of the resultant vector R is, R x = A x + B x = 18 + 10

Mylab Math With Pearson Etext -- 18 Week Standalone Access Card -- For Basic Technical Mathematics With Calculus

11th Edition

ISBN: 9780135902912

Author: Allyn J. Washington

Publisher: PEARSON

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Chapter 9.3, Problem 15E

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The resultant vector R and standard position angle θ by adding the components A=18,θA=0.0°,B=12.0 and θB=27.0°.

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Chapter 9.3, Problem 14E

Chapter 9.3, Problem 16E

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Chapter 9 Solutions

Mylab Math With Pearson Etext -- 18 Week Standalone Access Card -- For Basic Technical Mathematics With Calculus

Ch. 9.1 - For the vectors in Example 2, show that R = B + C...Ch. 9.1 - Prob. 2PE Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E Ch. 9.1 - Prob. 8E

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The resultant vector R and standard position angle θ by adding the components A = 18 , θ A = 0.0 ° , B = 12.0 and θ B = 27.0 ° .

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The resultant vector R and standard position angle θ by adding the components A=18,θA=0.0°,B=12.0 and θB=27.0°.

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