Explanation Given: The vector force F is { − 40 k } lb . Establish a position vector from O to A . The coordinate of the point A ( 3 , 5 , − 3 ) ft , and O ( 0 , 0 , 0 ) ft . Calculate the unit vector in the direction of OA is u O A . u O A = r O A r O A = ( x A − x O ) i + ( y A − y O ) j + ( z A − z O ) k ( x A − x O ) 2 + ( y A − y O ) 2 + ( z A − z O ) 2 (I) Here, the position vector r in the direction of OA is r O A , the length of the cable O A is r O A , and the coordinates of O and A in x , y and z directions are x O , x A , y O , y A , z O , and z A , respectively. Calculate the magnitude of component vector force F 1 . F 1 = F ⋅ u O A (II) Calculate the magnitude of component vector force F 2 . F 2 = ( F ) 2 − ( F 1 ) 2 (III) Conclusion: Substitute 3 ft for x A , 5 ft for y A , − 3 ft for z A , 0 ft for x O , 0 ft for y O , and 0 ft for z O in Equation (I)

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Chapter 2.9, Problem 119P

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The magnitudes of the components vector forces F1 and F2 directed along the pipe’s axis and perpendicular to it.

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Chapter 2.9, Problem 118P

Chapter 2.9, Problem 120P

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The magnitudes of the components vector forces F 1 and F 2 directed along the pipe’s axis and perpendicular to it.

Solution Summary: The author determines the magnitudes of the components vector forces directed along the pipe's axis and perpendicular to it.

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The magnitudes of the components vector forces F1 and F2 directed along the pipe’s axis and perpendicular to it.

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