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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
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.
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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