Express each result of Parts 1-5 in the form of a Cartesian vector. Part 4 requires the specification of 2 cartesian vectors: a force and a moment vector. **Engineering Statics Problem Set**1. **Determine the unit vector \( \vec{e}_{CD} \) in the direction from point C towards point D** - (which is the direction of the force \( \vec{F} \) of the figure).2. **Determine the moment \( \vec{M}_D \) of the force \( \vec{F} \) about the point D.**3. **Determine the moment \( \vec{M}_A \) of the force \( \vec{F} \) about the point A.**4. **Give the Force-Couple system which acts at point A, which is equivalent to the force \( \vec{F} \) given in the figure.**5. **Determine the unit vector \( \vec{e}_{AB} \) in the direction from point A towards point B.**6. **Determine the moment \( M_{AB} \) (as a scalar) which acts about the AB axis (i.e., the line from point A toward B) due to the force \( \vec{F} \).**---For the above exercises, ensure that you carefully denote the vectors and moments as specified, and provide detailed solutions for calculating the unit vectors and moments. The force-couple system requires thorough understanding of the equivalent systems in statics. ### Educational Content: Analysis of Force on a Structural Member#### Description:The diagram shows a structural member subjected to a force \( \mathbf{F} \) of 700 N. The system is represented in a three-dimensional coordinate system with coordinates \( x \), \( y \), and \( z \). The force \( \mathbf{F} \) is applied at point \( C \) and is aligned along the line connecting points \( C \) and \( D \).#### Key Points:- **Force:** \( \mathbf{F} = 700 \, \text{N} \)- **Coordinate System:** - \( x \)-axis is horizontal in the diagram, directed to the left. - \( y \)-axis is horizontal in the diagram, directed upward. - \( z \)-axis is vertical.- **Main Structural Points:** - **Point A:** The origin where the three axes intersect. - **Point B:** Another reference point placed at coordinates \((0.4, 0.2, 0)\). - **Point C:** The point of force application, which is at \((0.6, 0, 0.3)\). - **Point D:** The terminal point that lies in the line of action of force, which is at \((0, 0.2, 0)\).#### Dimensions:- The distance between points is marked as follows: - The horizontal distance between point \( B \) and the \( y \)-axis is \( 0.4 \, \text{m} \). - The vertical distance from point \( A \) to point \( C \) is \( 0.3 \, \text{m} \). - The projection of the distance from point \( A \) horizontally to point \( D \) is \( 0.2 \, \text{m} \).#### Notes:- Points \( C \) and \( D \) lie on the line of action of the force \( \mathbf{F} \), indicating that the force vector passes through these points in space.#### Coordinates (in meters):- **Point A:** \( (0, 0, 0) \)- **Point B:** \( (0.4, 0.2, 0) \)- **Point C:** \( (0.6, 0

According to company policy, we are restricted to solve only the first three sub-part of one…

1. Determine the unit vector heo in the direction from pointe touids point D. (which is the I direction of the Force Fof the figue, 2. Determine the Moment Mo of the the force F about the point Do point Da 3, Determine the moment MA of the force Ê about the point A.

1. Determine the unit vector heo in the direction from pointe touids point D. (which is the I direction of the Force Fof the figue, 2. Determine the Moment Mo of the the force F about the point Do point Da 3, Determine the moment MA of the force Ê about the point A.

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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Question

Express each result of Parts 1-5 in the form of a Cartesian vector. Part 4 requires the specification of 2 cartesian vectors: a force and a moment vector.

**Engineering Statics Problem Set**

1. **Determine the unit vector \( \vec{e}_{CD} \) in the direction from point C towards point D**
- (which is the direction of the force \( \vec{F} \) of the figure).

2. **Determine the moment \( \vec{M}_D \) of the force \( \vec{F} \) about the point D.**

3. **Determine the moment \( \vec{M}_A \) of the force \( \vec{F} \) about the point A.**

4. **Give the Force-Couple system which acts at point A, which is equivalent to the force \( \vec{F} \) given in the figure.**

5. **Determine the unit vector \( \vec{e}_{AB} \) in the direction from point A towards point B.**

6. **Determine the moment \( M_{AB} \) (as a scalar) which acts about the AB axis (i.e., the line from point A toward B) due to the force \( \vec{F} \).**

---

For the above exercises, ensure that you carefully denote the vectors and moments as specified, and provide detailed solutions for calculating the unit vectors and moments. The force-couple system requires thorough understanding of the equivalent systems in statics.

### Educational Content: Analysis of Force on a Structural Member

#### Description:

The diagram shows a structural member subjected to a force \( \mathbf{F} \) of 700 N. The system is represented in a three-dimensional coordinate system with coordinates \( x \), \( y \), and \( z \). The force \( \mathbf{F} \) is applied at point \( C \) and is aligned along the line connecting points \( C \) and \( D \).

#### Key Points:

- **Force:** \( \mathbf{F} = 700 \, \text{N} \)
- **Coordinate System:**
- \( x \)-axis is horizontal in the diagram, directed to the left.
- \( y \)-axis is horizontal in the diagram, directed upward.
- \( z \)-axis is vertical.
- **Main Structural Points:**
- **Point A:** The origin where the three axes intersect.
- **Point B:** Another reference point placed at coordinates \((0.4, 0.2, 0)\).
- **Point C:** The point of force application, which is at \((0.6, 0, 0.3)\).
- **Point D:** The terminal point that lies in the line of action of force, which is at \((0, 0.2, 0)\).

#### Dimensions:

- The distance between points is marked as follows:
- The horizontal distance between point \( B \) and the \( y \)-axis is \( 0.4 \, \text{m} \).
- The vertical distance from point \( A \) to point \( C \) is \( 0.3 \, \text{m} \).
- The projection of the distance from point \( A \) horizontally to point \( D \) is \( 0.2 \, \text{m} \).

#### Notes:

- Points \( C \) and \( D \) lie on the line of action of the force \( \mathbf{F} \), indicating that the force vector passes through these points in space.

#### Coordinates (in meters):

- **Point A:** \( (0, 0, 0) \)
- **Point B:** \( (0.4, 0.2, 0) \)
- **Point C:** \( (0.6, 0

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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