### Problem Statement4) Determine the total moment caused by the forces \( F_{DA} \) and \( F_{CA} \) about the plate diagonal that goes through point \( B \) (the dashed line). Write your answer in Cartesian vector notation.### Diagram DescriptionIn the provided diagram:- There is a triangular plate resting on the XY plane. - The vertices of the plate are labeled as \( A \), \( B \), \( C \), and \( D \).- The point \( A \) is elevated above the XY plane. - The coordinates of the points on the XY plane are: - \( B \) is located 3 ft along the X-axis from the origin, - \( C \) is located 6 ft along the X-axis and 3 ft along the Y-axis from the origin, - \( D \) is located 3 ft along the X-axis and 3 ft along the Y-axis from the origin.- The point \( A \) is elevated 14 ft above point \( C \).**Forces:**- \( F_{BA} \) is 350 lb acting along line segment \( BA \).- \( F_{DA} \) is 400 lb acting along line segment \( DA \).- \( F_{CA} \) is 500 lb acting along line segment \( CA \).### Steps to Determine the Moment in Cartesian Vector Notation:To solve this, follow the steps below:1. **Determine Position Vectors:** - Determine the position vectors for points \( B \), \( C \), \( D \), and \( A \) relative to the origin.2. **Express Forces in Cartesian Coordinates:** - Write the forces \( F_{DA} \) and \( F_{CA} \) in Cartesian vector form.3. **Calculate Cross Product:** - Compute the moments produced by each of the forces about the diagonal through point \( B \).4. **Sum the Moments:** - Sum the moments to find the total moment about the specified axis.Following this procedure will lead you to the desired total moment in Cartesian vector notation.This type of problem helps to enhance understanding of vector operations and moment calculations, which are crucial for solving more complex engineering mechanics problems.

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4) Determine the total moment caused by the forces FDA and Fca about the plate diagonal that goes through point B (the dashed line). Write your answer in cartesian vector notation.

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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Concept explainers

Basic Terminology in Mechanics

The area of science and mathematics concerned the motion of the objects, the relation between the force matter, and motion if specified. Forces exerted over the objects result in displacements or changes in the position of an object concerning its environment. This branch of physics keeps its roots in Ancient Greece in the form of the scripts of Aristotle and Archimedes.

Question

### Problem Statement
4) Determine the total moment caused by the forces \( F_{DA} \) and \( F_{CA} \) about the plate diagonal that goes through point \( B \) (the dashed line). Write your answer in Cartesian vector notation.

### Diagram Description
In the provided diagram:

- There is a triangular plate resting on the XY plane.
- The vertices of the plate are labeled as \( A \), \( B \), \( C \), and \( D \).
- The point \( A \) is elevated above the XY plane.
- The coordinates of the points on the XY plane are:
- \( B \) is located 3 ft along the X-axis from the origin,
- \( C \) is located 6 ft along the X-axis and 3 ft along the Y-axis from the origin,
- \( D \) is located 3 ft along the X-axis and 3 ft along the Y-axis from the origin.
- The point \( A \) is elevated 14 ft above point \( C \).

**Forces:**
- \( F_{BA} \) is 350 lb acting along line segment \( BA \).
- \( F_{DA} \) is 400 lb acting along line segment \( DA \).
- \( F_{CA} \) is 500 lb acting along line segment \( CA \).

### Steps to Determine the Moment in Cartesian Vector Notation:

To solve this, follow the steps below:

1. **Determine Position Vectors:**
- Determine the position vectors for points \( B \), \( C \), \( D \), and \( A \) relative to the origin.

2. **Express Forces in Cartesian Coordinates:**
- Write the forces \( F_{DA} \) and \( F_{CA} \) in Cartesian vector form.

3. **Calculate Cross Product:**
- Compute the moments produced by each of the forces about the diagonal through point \( B \).

4. **Sum the Moments:**
- Sum the moments to find the total moment about the specified axis.

Following this procedure will lead you to the desired total moment in Cartesian vector notation.

This type of problem helps to enhance understanding of vector operations and moment calculations, which are crucial for solving more complex engineering mechanics problems.

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