In the 3D spatial problem below, force F is represented by dimension locations and has a magnitude of 90.0 lbs on the end of the pipe segment as shown.a. Define the position vector AD.b. Define the Cartesian Force vector for the force F of 90.0 lbs.c. Calculate the direction cosines (α, β, and γ) of the force F.d. Determine the moment produced by the force F about the origin, A. (use the position vector from A to D.)e. Determine the moment produced by force F about wire AC of the pipe assembly. Express the result as a Cartesian vector and as a magnitude.f. What is the angle between the force vector and the wire AC?**Diagram Explanation:**The diagram illustrates a pipe segment in a 3D coordinate system defined by the axes X, Y, and Z. The following points and measurements are noted:- **Point A** is aligned on the Z-axis, 4 inches above point B on the Y-axis. - **Point B** is 3 inches along the Y-axis from point C.- **Point D** is located at the bottom, 5 inches downward from point C, extending 4 inches along the X-axis, and 7 inches further along the X-axis from the origin (for a total of 11 inches from the origin considering the segments).- **Force F** of 90 lbs acts at an angle from point D, represented by a dashed line pointing towards point E, 4 inches along X and 4 inches along Y from D.The task is to use these geometric and force specifications to determine vectors, Cartesian components, direction cosines, moments, and angles concerning the assembly's specific segments and points.

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Answered: a. Define the position vector AD. b.…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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a. Define the position vector AD. b. Define the Cartesian Force vector for the force F of 90.0 lbs. c. Calculate the direction cosines (a,B,and y) of the force F.