A force is defined by the vector A= 3.5i- 1.5j+2.0k. What is the angle that the forces make with the positive y-axis? O 69.6° O 20 49
A force is defined by the vector A= 3.5i- 1.5j+2.0k. What is the angle that the forces make with the positive y-axis? O 69.6° O 20 49
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
Related questions
Question
![### Problem Statement
A force is defined by the vector **A = 3.5i - 1.5j + 2.0k**. What is the angle that the forces make with the positive y-axis?
### Options
- **69.6°**
- **20.4°**
- **110°**
- **66.4°**
### Explanation
To solve this problem, you need to determine the angle between the vector **A** and the positive y-axis. This involves using the dot product and the magnitudes of the vectors.
1. **Vector Components**:
- **A = 3.5i - 1.5j + 2.0k**
2. **Dot Product Formula**:
\[
A \cdot j = |A| \cdot |j| \cdot \cos(\theta)
\]
Since **j = 0i + 1j + 0k**:
\[
A \cdot j = -1.5
\]
3. **Magnitude of Vector A**:
\[
|A| = \sqrt{(3.5)^2 + (-1.5)^2 + (2.0)^2}
\]
4. **Solve for \(\theta\)**:
\[
\cos(\theta) = \frac{-1.5}{|A|}
\]
\[
\theta = \cos^{-1}\left(\frac{-1.5}{|A|}\right)
\]
After calculating, you'll find the correct angle from the available options.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9bf7f6f8-9470-47f0-a3a4-f3c052528216%2F97c5dc54-e031-4f4e-a919-528d58b04737%2Fe6d3c0f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
A force is defined by the vector **A = 3.5i - 1.5j + 2.0k**. What is the angle that the forces make with the positive y-axis?
### Options
- **69.6°**
- **20.4°**
- **110°**
- **66.4°**
### Explanation
To solve this problem, you need to determine the angle between the vector **A** and the positive y-axis. This involves using the dot product and the magnitudes of the vectors.
1. **Vector Components**:
- **A = 3.5i - 1.5j + 2.0k**
2. **Dot Product Formula**:
\[
A \cdot j = |A| \cdot |j| \cdot \cos(\theta)
\]
Since **j = 0i + 1j + 0k**:
\[
A \cdot j = -1.5
\]
3. **Magnitude of Vector A**:
\[
|A| = \sqrt{(3.5)^2 + (-1.5)^2 + (2.0)^2}
\]
4. **Solve for \(\theta\)**:
\[
\cos(\theta) = \frac{-1.5}{|A|}
\]
\[
\theta = \cos^{-1}\left(\frac{-1.5}{|A|}\right)
\]
After calculating, you'll find the correct angle from the available options.
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