Explanation Establish a position vector for points A , B , and C . The coordinates are: point A ( 0 , 3 , 0 ) ft , point B ( 2 , 2 , 2 ) ft , and point C ( 0 , 0 , 0 ) ft. Express the position vector r in the direction of AB . r A B = ( x B − x A ) i + ( y B − y A ) j + ( z B − z A ) k (I) Here, the coordinates of A and B are x A , x B , y A , y B , z A , and z B , respectively. Express the position vector r in the direction of AC . r A C = ( x C − x A ) i + ( y C − y A ) j + ( z C − z A ) k (II) Here, the coordinates of A and C are x A , x C , y A , y C , z A , and z C , respectively. Express the magnitude of the direction of AB . r A B = ( x B − x A ) 2 + ( y B − y A ) 2 + ( z B − z A ) 2 (III) Express the magnitude of the direction of AC . r A C = ( x C − x A ) 2 + ( y C − y A ) 2 + ( z C − z A ) 2 (IV) Determine the unit vector of AB . u A B = ( r A B r A B ) (V) Here, the position vector in the direction of AB is r A B , and the magnitude of the position vector in the direction of AB is r A B . Determine the unit vector of AC . u A C = ( r A C r A C ) (VI) Here, the position vector in the direction of AC is r A C , and the magnitude of the position vector in the direction of AC is r A C . Apply the dot product to find the angle between two cables. u A B ⋅ u A C = cos θ θ = cos − 1 ( u A B ⋅ u A C ) (VII) Conclusion: Substitute 0 ft for x A , 3 ft for y A , 0 ft for z A , 2 ft for x B , 2 ft for y B , and 2 ft for z B in Equation (I). r A B = ( 0 − 2 ) i + ( 3 − 2 ) j + ( 0 − 2 ) k = − 2 i + 1 j − 2 k Substitute 0 ft for x C , 0 ft for y C , 0 ft for z C , 0 ft for x A , 3 ft for y A , and 0 ft for z A in Equation (II)

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 2.9, Problem 116P

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The angle θ between the y-axis of the pole and the wire AB.

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Chapter 2.9, Problem 115P

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Engineering Mechanics: Statics & Dynamics (14th Edition)

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The angle θ between the y -axis of the pole and the wire AB .

Solution Summary: The author determines the angle between the y -axis of the pole and the wire AB. Establish a position vector for points A, B, and C.

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The angle θ between the y-axis of the pole and the wire AB.

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