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 vector A = 21.9 is directed at an angle θ A = 236.2 ° , B = 96.7 is directed at an angle θ B = 11.5 ° and C = 62.9 is directed at an angle θ C = 143.4 ° . 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 . Then, the x component of the resultant vector R is, R x = A x + B x + C x = A cos θ A + B cos θ B + C cos θ C = 21.9 cos 236.2 ° + 96.7 cos 11.5 ° + 62.9 cos 143.4 ° ≈ ( − 12.18 ) + 94.76 + ( − 50.5 ) ≈ 32.08 Similarly, the y component of the resultant vector R is, R y = A y + B y + C y = A sin θ A + B sin θ B + C sin θ C = 21

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Chapter 9.3, Problem 23E

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The resultant vector R and standard position angle θ by adding the components A=21.9,θA=236.2°,B=96.7,θB=11.5° and C=62.9,θC=143.4°.

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Chapter 9.3, Problem 22E

Chapter 9.3, Problem 24E

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Chapter 9 Solutions

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

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 = 21.9 , θ A = 236.2 ° , B = 96.7 , θ B = 11.5 ° and C = 62.9 , θ C = 143.4 ° .

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The resultant vector R and standard position angle θ by adding the components A=21.9,θA=236.2°,B=96.7,θB=11.5° and C=62.9,θC=143.4°.

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