Explanation Draw the free body diagram of forces F B and F C from point A as in Figure (1). Establish a position vector from A to B to A to C . The coordinates of the points A, B, C are A ( 2 , 0 , 6 ) m , B ( 0 , 4 , 2 ) m and point C ( − 4 , 3 , 4 ) m . Express the position vector r in the direction of AB using Figure (1). 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 using Figure (1). 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 C , x A , y C , y A , z C , and z A , respectively. Express the force F B as a Cartesian vector form and position vector r directed from point A to point B . F B = F B u A B = F B ( r A B r A B ) = F B ( r A B ( x B − x A ) 2 + ( y B − y A ) 2 + ( z B − z A ) 2 ) (III) Here, the unit vector in the direction of AB is u A B , position vector in the direction of AB is r A B , and magnitude of the position vector in the direction of AB is r A B . Express the force F C as a Cartesian vector form and position vector r directed from point A to point C . F C = F C u A C = F C ( r A C r A C ) = F C ( r A C ( x C − x A ) 2 + ( y C − y A ) 2 + ( z C − z A ) 2 ) (IV) Here, the unit vector in the direction of AC is u A C , position vector in the direction of AC is r A C , and magnitude of the position vector in the direction of AC is r A C . Determine the resultant force at point A . F R = F B + F C (V) Conclusion: Substitute 0 ft for x B , 4 ft for y B , 2 ft for z B , 2 ft for x A , 0 for y A , and 6 ft for z A in Equation (I). r A B = ( 0 − 2 ) i + ( 4 − 0 ) j + ( 2 − 6 ) k = { − 2 i + 4 j − 4 k } ft Substitute 4 ft for x C , 3 ft for y C , 4 ft for z C , 2 ft for x A , 0 for y A , and 6 ft for z A in Equation (II)

MOD.MASTER.W/ETEXT ENG.MECHANICS CARD+BK

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ISBN: 9780137519170

Author: HIBBELER

Publisher: PEARSON

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MOD.MASTER.W/ETEXT ENG.MECHANICS CARD+BK

Ch. 2 - Determine the magnitude of the resultant force...Ch. 2 - Two forces act on the hook. Determine the...Ch. 2 - Determine the magnitude of the resultant force and...Ch. 2 - Resolve the 30-lb force into components along the...Ch. 2 - The force F = 450 lb acts on the frame. Resolve...Ch. 2 - If force F is to have a component along the u axis...Ch. 2 - Determine the magnitude of the resultant force FR...Ch. 2 - Resolve the force F1 into components acting along...Ch. 2 - Resolve the force F2 into components acting along...Ch. 2 - Prob. 10P

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Solution Summary: The author explains how to determine the resultant force at A. Draw a free body diagram of forces from A to B and express the position vector r in the direction of AC.

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