Explanation Establish a position vector for points A , B , and C . The coordinates are: point A ( 0 , − 2 , 0 ) m , point B ( 0 , 0 , 0 ) m , and point C ( 3 , 4 , − 1 ) m. Express the position vector r in the direction of BA . r B A = ( x A − x B ) i + ( y A − y B ) j + ( z A − z B ) 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 BC . r B C = ( x C − x B ) i + ( y C − y B ) j + ( z C − z B ) k (II) Here, the coordinates of B and C are x B , x C , y B , y C , z B , and z C , respectively. Express the magnitude of the direction of BA . r B A = ( x A − x B ) 2 + ( y A − y B ) 2 + ( z A − z B ) 2 (III) Express the magnitude of the direction of BC . r B C = ( x C − x B ) 2 + ( y C − y B ) 2 + ( z C − z B ) 2 (IV) Determine the unit vector of BA . u B A = ( r B A r B A ) (V) Here, the position vector in the direction of BA is r B A , and the magnitude of the position vector in the direction of BA is r B A . Determine the unit vector of BC . u B C = ( r B C r B C ) (VI) Here, the position vector in the direction of BC is r B C , and the magnitude of the position vector in the direction of BC is r B C . Apply the dot product to find the angle between two cables. u B A ⋅ u B C = cos θ θ = cos − 1 ( u B A ⋅ u B C ) (VII) Conclusion: Substitute 0 m for x A , 2 m for y A , 0 m for z A , 0 m for x B , 0 m for y B , and 0 m for z B in Equation (I). r B A = ( 0 − 0 ) i + ( − 2 − 0 ) j + ( 0 − 0 ) k = ( − 2 j ) m Substitute 3 m for x C , 4 m for y C , 1 m for z C , 0 m for x B , 0 m for y B , and 0 m for z B 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 128P

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The angle θ between BA and BC.

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Chapter 2.9, Problem 127P

Chapter 2.9, Problem 129P

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The angle θ between BA and BC .

Solution Summary: The author determines the angle theta between BA and BC. Establish a position vector for points A, B, and C.

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The angle θ between BA and BC.

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