Explanation Establish a position vector for points A , B , and C . The coordinates are: point A ( 0 , 0 , 1 ) m , point B ( 0 , 2 , 4 ) m , and point C ( 3 , 4 , 0 ) m. 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) Apply the dot product to find the angle between the two cables. u A B ⋅ u A C = cos θ θ = cos − 1 ( u A B ⋅ u A C ) (VII) Conclusion: Substitute 0 m for x A , 0 m for y A , 1 m for z A , 0 m for x B , 2 m for y B , and 4 m for z B in Equation (I). r A B = ( 0 − 0 ) i + ( 2 − 0 ) j + ( 4 − 1 ) k = ( 0 i + 2 j + 3 k ) m Substitute 3 m for x C , 4 m for y C , 0 m for z C , 0 m for x A , 0 m for y A , and 1 m for z A in Equation (II)

Engineering Mechanics: Statics and Study Pack (13th Edition)

13th Edition

ISBN: 9780133027990

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 2.9, Problem 114P

To determine

The angle θ between AB and AC.

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Chapter 2.9, Problem 113P

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Chapter 2 Solutions

Engineering Mechanics: Statics and Study Pack (13th Edition)

Ch. 2.3 - Determine the magnitude of the resultant force...Ch. 2.3 - Determine the magnitude of the resultant force....Ch. 2.3 - Determine the magnitude of the resultant force and...Ch. 2.3 - Resolve the 30-lb force into components along the...Ch. 2.3 - Resolve this force into components acting along...Ch. 2.3 - along the v axis. Prob. F2-6 Ch. 2.3 - Determine the magnitude of the resultant force FR...Ch. 2.3 - If = 60 and F = 450 N, determine the magnitude of...Ch. 2.3 - If the magnitude of the resultant force is to be...Ch. 2.3 - Determine the magnitude of the resultant force FR...

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The angle θ between AB and AC .

The angle θ between AB and AC.

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Chapter 2 Solutions