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The force F = {-100i+200j +200k} N. The moment of F about the line from O to A is MOA = {470i +315j + 160k} Nm. What are the direction cosines of the position vector ra/o? Answer: cos0x=0.800, cos0y= 0.536, cos0z= 0.272 (-2,6,3) m FOA

The force F = {-100i+200j +200k} N. The moment of F about the line from O to A is MOA = {470i +315j + 160k} Nm. What are the direction cosines of the position vector ra/o? Answer: cos0x=0.800, cos0y= 0.536, cos0z= 0.272 (-2,6,3) m FOA

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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The force **F** is given by **F** = {-100i + 200j + 200k} N. The moment of **F** about the line from O to A is **M_OA** = {470i + 315j + 160k} Nm. What are the direction cosines of the position vector **r_A/O**? **Answer:** cosθₓ = 0.800, cosθ_y = 0.536, cosθ_z = 0.272 **Diagram Explanation:** The diagram illustrates a coordinate system with x, y, and z axes. There are two vectors: - Vector **F** is shown in the space with components (-2, 6, 3) meters. - Vector **r_OA** extends from point O to point A, indicating the position vector for which the direction cosines are to be determined. The diagram visually represents the spatial relation of vector **F** and the line OA along the axes, facilitating the calculation of direction cosines using the provided force and moment vectors.
Transcribed Image Text:The force **F** is given by **F** = {-100i + 200j + 200k} N. The moment of **F** about the line from O to A is **M_OA** = {470i + 315j + 160k} Nm. What are the direction cosines of the position vector **r_A/O**? **Answer:** cosθₓ = 0.800, cosθ_y = 0.536, cosθ_z = 0.272 **Diagram Explanation:** The diagram illustrates a coordinate system with x, y, and z axes. There are two vectors: - Vector **F** is shown in the space with components (-2, 6, 3) meters. - Vector **r_OA** extends from point O to point A, indicating the position vector for which the direction cosines are to be determined. The diagram visually represents the spatial relation of vector **F** and the line OA along the axes, facilitating the calculation of direction cosines using the provided force and moment vectors.
Expert Solution
Step 1

Objective: To determine the direction cosines for the position vector rA/O.

 

Given:

F=-100i+200j+200k N

MOA=470i+315j+160k Nm

 

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