**Crane Force and Moment Analysis**The boom of a crane extends from its base at point \( O \) to its tip at point \( Q \), as illustrated in the figure. The figure displays a three-dimensional coordinate system with coordinates for \( O = (0, 0, 0) \) and \( Q = (-2, 10, 10) \) feet. A force \( \mathbf{F} \) with a magnitude of 10.5 kip is applied at the tip of the boom by a cable that extends from point \( Q \) to point \( P \) in the x–y plane, with coordinates \( P = (9, 6, 0) \) feet.### Diagram Explanation:- **Axes**: The diagram shows a three-dimensional coordinate system with \( x \), \( y \), and \( z \) axes intersecting at point \( O \).- **Boom**: The crane's boom is represented as a line extending from \( O \) to \( Q \).- **Force \(\mathbf{F}\)**: Illustrated as a vector applied at point \( Q \), directed along the cable towards point \( P \).### Problem Requirements:Determine the following quantities:**(a) The force \(\mathbf{F}\) as a Cartesian vector:**\[ \mathbf{F} = \text{number} \, \mathbf{i} + \text{number} \, \mathbf{j} + \text{number} \, \mathbf{k} \, \text{kip}\]**(b) The moment \(\mathbf{M}_O\) due to force \(\mathbf{F}\) about point \( O \):**\[ \mathbf{M}_O = \text{number} \, \mathbf{i} + \text{number} \, \mathbf{j} + \text{number} \, \mathbf{k} \, \text{kip} \cdot \text{ft}\]**(c) The magnitude of moment \(\mathbf{M}_O\):**\[ M_O = \text{number} \, \text{kip} \cdot \text{ft}\]

According to given data, o(0,0,0)P(9,6,0)Q(-2,10,10)so, QP→=(9+2)i+(6-10)j-10k=11i-4j-10kunit vector…

The boom of a crane extends from its base at point O to its tip at point Q, as shown in the figure below. A three-dimensional coordinate system is given in this figure with coordinates for both points of O = (0,0,0) and Q = (-2, 10, 10) ft. A force with a magnitude of 10.5 kip is applied at the tip of the boom by a cable that extends from point Q to point P in the x-y plane, which has coordinates P = (9,6, 0) ft. Determine the following quantities:

The boom of a crane extends from its base at point O to its tip at point Q, as shown in the figure below. A three-dimensional coordinate system is given in this figure with coordinates for both points of O = (0,0,0) and Q = (-2, 10, 10) ft. A force with a magnitude of 10.5 kip is applied at the tip of the boom by a cable that extends from point Q to point P in the x-y plane, which has coordinates P = (9,6, 0) ft. Determine the following quantities:

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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