If Force (-2,3) and Displacement (-5,-3), find the angle in degrees between the two vectors. O 18.61 deg O 160 deg O 48.94 deg . O 87.27 deg O 32.16 deg
If Force (-2,3) and Displacement (-5,-3), find the angle in degrees between the two vectors. O 18.61 deg O 160 deg O 48.94 deg . O 87.27 deg O 32.16 deg
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![**Problem Statement:**
Given:
- Force vector \( \mathbf{F} = (-2, 3) \)
- Displacement vector \( \mathbf{D} = (-5, -3) \)
**Question:**
Find the angle in degrees between these two vectors.
**Options:**
- 18.61 degrees
- 160 degrees
- 48.94 degrees
- 87.27 degrees
- 32.16 degrees
To solve this problem, use the formula for the angle \(\theta\) between two vectors \(\mathbf{A}\) and \(\mathbf{B}\):
\[
\cos \theta = \frac{\mathbf{A} \cdot \mathbf{B}}{\|\mathbf{A}\| \|\mathbf{B}\|}
\]
Where:
- \(\mathbf{A} \cdot \mathbf{B}\) is the dot product of the vectors.
- \(\|\mathbf{A}\|\) and \(\|\mathbf{B}\|\) are the magnitudes of the vectors.
Follow these steps:
1. Compute the dot product of \(\mathbf{F}\) and \(\mathbf{D}\).
2. Find the magnitudes of \(\mathbf{F}\) and \(\mathbf{D}\).
3. Use the angle formula to find \(\theta\).
4. Convert the angle from radians to degrees if necessary.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fde10ac4d-a71c-4404-a6a7-5da9829e3a85%2Fea4149a9-e4ca-445d-aa52-fcbe106df892%2Fc7bk4bf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Given:
- Force vector \( \mathbf{F} = (-2, 3) \)
- Displacement vector \( \mathbf{D} = (-5, -3) \)
**Question:**
Find the angle in degrees between these two vectors.
**Options:**
- 18.61 degrees
- 160 degrees
- 48.94 degrees
- 87.27 degrees
- 32.16 degrees
To solve this problem, use the formula for the angle \(\theta\) between two vectors \(\mathbf{A}\) and \(\mathbf{B}\):
\[
\cos \theta = \frac{\mathbf{A} \cdot \mathbf{B}}{\|\mathbf{A}\| \|\mathbf{B}\|}
\]
Where:
- \(\mathbf{A} \cdot \mathbf{B}\) is the dot product of the vectors.
- \(\|\mathbf{A}\|\) and \(\|\mathbf{B}\|\) are the magnitudes of the vectors.
Follow these steps:
1. Compute the dot product of \(\mathbf{F}\) and \(\mathbf{D}\).
2. Find the magnitudes of \(\mathbf{F}\) and \(\mathbf{D}\).
3. Use the angle formula to find \(\theta\).
4. Convert the angle from radians to degrees if necessary.
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