The displacement vectors A and B shown in the figure below both have magnitudes of 1.70 m. The direction of vector A is 0 = 34.0°. (a) Find A + B graphically. magnitude 3.002 m direction 62 ° counterclockwise from the +x axis (b) Find A – graphically. magnitude 1.596 m direction 332 ° counterclockwise from the +x axis (c) Find B – A graphically. magnitude 1.596 m direction 152 ° counterclockwise from the +x axis (d) Find A – 2B graphically. magnitude 2.825 direction | 422 X ° counterclockwise from the +x axis

The displacement vectors A and B shown in the figure below both have magnitudes of 1.70 m. The direction of vector A is 0 = 34.0°. (a) Find A + B graphically. magnitude 3.002 m direction 62 ° counterclockwise from the +x axis (b) Find A – graphically. magnitude 1.596 m direction 332 ° counterclockwise from the +x axis (c) Find B – A graphically. magnitude 1.596 m direction 152 ° counterclockwise from the +x axis (d) Find A – 2B graphically. magnitude 2.825 direction | 422 X ° counterclockwise from the +x axis

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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Question

The displacement vectors \(\vec{A}\) and \(\vec{B}\) shown in the figure both have magnitudes of 1.70 m. The direction of vector \(\vec{A}\) is \(\theta = 34.0^\circ\).

**Diagram Explanation:**
The figure displays a coordinate system with vectors \(\vec{A}\) and \(\vec{B}\). Vector \(\vec{B}\) is aligned along the y-axis, and vector \(\vec{A}\) is at an angle \(\theta\) of 34.0 degrees from the x-axis.

### Tasks:

**(a) Find \(\vec{A} + \vec{B}\) graphically.**
- Magnitude: 3.002 m
- Direction: 62° counterclockwise from the +x axis

**(b) Find \(\vec{A} - \vec{B}\) graphically.**
- Magnitude: 1.596 m
- Direction: 332° counterclockwise from the +x axis

**(c) Find \(\vec{B} - \vec{A}\) graphically.**
- Magnitude: 1.596 m
- Direction: 152° counterclockwise from the +x axis

**(d) Find \(\vec{A} - 2\vec{B}\) graphically.**
- Magnitude: 2.825 m
- Direction: 422° counterclockwise from the +x axis (Note: The direction should be simplified to within 360° if necessary)

These solutions involve vector addition and subtraction, demonstrating their results in both magnitude and direction as measured counterclockwise from the positive x-axis.

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