### Problem 2/90: Microwave Transmission Tower Stability#### Description:A 70-meter high microwave transmission tower is stabilized by three guy cables, as illustrated in the diagram.#### Scenario:- **Cable AB** carries a tension of 12 kN.- The objective is to express the corresponding force on point B as a vector.#### Diagram Explanation:1. **3D Ground Plane Representation**: - The setup is depicted in a 3-dimensional coordinate system with axes labeled \(x\), \(y\), and \(z\). - The origin, point **O**, is at the base of the tower.2. **Tower**: - The tower extends vertically upward along the **z-axis**, reaching a height of 70 meters, known as point **A**.3. **Guy Cables**: - **Cable AB** extends from the top of the tower (point **A**) to the ground at point **B**. - The positions of points **B, C,** and **D** are given in the **xy-plane** relative to point **O** (origin).4. **Coordinates and Positions**: - **Point A**: (0, 0, 70) - **Point O**: (0, 0, 0) - **Point B**: (-20, -25, 0). This means point **B** is 20 meters along the negative \(x\)-axis and 25 meters along the negative \(y\)-axis from the origin.#### Task:To express the force exerted by cable AB on point B as a vector, using the given coordinate information and tension value.#### Solution Outline:1. **Determine Position Vector \( \overrightarrow{AB} \)**: - Calculate the components of vector \( \overrightarrow{AB} \) in the \(x, y, z\) coordinates. - \( \overrightarrow{AB} = B - A = (-20 - 0, -25 - 0, 0 - 70) = (-20, -25, -70) \).2. **Calculate the Magnitude of \( \overrightarrow{AB} \)**: - \( | \overrightarrow{AB} | = \sqrt{(-20)^2 + (-25)^2 + (-70)^2} \).3. **Determine Unit Vector \( \hat

Solution: Co ordinates of the points are : A = (0,0,70)B=(35,-25,10)C = (20, 50,0)D = (-40, 20,0)

2/90 The 70-m microwave transmission tower is steadied by three guy cables as shown. Cable AB carries a tension of 12 kN. Express the corresponding force on point B as a vector. z 35 m 40 m B 25 m A 70 m 10 m 20 m 30 m C 20 m y

2/90 The 70-m microwave transmission tower is steadied by three guy cables as shown. Cable AB carries a tension of 12 kN. Express the corresponding force on point B as a vector. z 35 m 40 m B 25 m A 70 m 10 m 20 m 30 m C 20 m y

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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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 2/90: Microwave Transmission Tower Stability

#### Description:

A 70-meter high microwave transmission tower is stabilized by three guy cables, as illustrated in the diagram.

#### Scenario:

- **Cable AB** carries a tension of 12 kN.
- The objective is to express the corresponding force on point B as a vector.

#### Diagram Explanation:

1. **3D Ground Plane Representation**:
- The setup is depicted in a 3-dimensional coordinate system with axes labeled \(x\), \(y\), and \(z\).
- The origin, point **O**, is at the base of the tower.

2. **Tower**:
- The tower extends vertically upward along the **z-axis**, reaching a height of 70 meters, known as point **A**.

3. **Guy Cables**:
- **Cable AB** extends from the top of the tower (point **A**) to the ground at point **B**.
- The positions of points **B, C,** and **D** are given in the **xy-plane** relative to point **O** (origin).

4. **Coordinates and Positions**:
- **Point A**: (0, 0, 70)
- **Point O**: (0, 0, 0)
- **Point B**: (-20, -25, 0). This means point **B** is 20 meters along the negative \(x\)-axis and 25 meters along the negative \(y\)-axis from the origin.

#### Task:

To express the force exerted by cable AB on point B as a vector, using the given coordinate information and tension value.

#### Solution Outline:

1. **Determine Position Vector \( \overrightarrow{AB} \)**:
- Calculate the components of vector \( \overrightarrow{AB} \) in the \(x, y, z\) coordinates.
- \( \overrightarrow{AB} = B - A = (-20 - 0, -25 - 0, 0 - 70) = (-20, -25, -70) \).

2. **Calculate the Magnitude of \( \overrightarrow{AB} \)**:
- \( | \overrightarrow{AB} | = \sqrt{(-20)^2 + (-25)^2 + (-70)^2} \).

3. **Determine Unit Vector \( \hat

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