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The three vectors in the figure have magnitudes a = 2.60 m, b = 2.80 m, and c = 10.1 m and angle - 31.0°. What are (a) the x component and (b) the y component of a; (c) the x component and (d) the y component of b; and (e) the x component and (f) the y component of ? If = pa+qb, what are the values of (g) p and (h) q?

The three vectors in the figure have magnitudes a = 2.60 m, b = 2.80 m, and c = 10.1 m and angle - 31.0°. What are (a) the x component and (b) the y component of a; (c) the x component and (d) the y component of b; and (e) the x component and (f) the y component of ? If = pa+qb, what are the values of (g) p and (h) q?

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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**Vector Components and Combinations: A Guide** The problem here involves three vectors with specific magnitudes and angles, and we need to determine their components in the x and y directions as well as their combinations. The given information: - Vector \(\vec{a}\) has a magnitude \(a = 2.60 \text{ m}\) - Vector \(\vec{b}\) has a magnitude \(b = 2.80 \text{ m}\) - Vector \(\vec{c}\) has a magnitude \(c = 10.1 \text{ m}\) - The angle between vector \(\vec{a}\) and the x-axis is \(\theta = 31.0^\circ\) The goal is to find the following: - (a) The x-component of \(\vec{a}\) - (b) The y-component of \(\vec{a}\) - (c) The x-component of \(\vec{b}\) - (d) The y-component of \(\vec{b}\) - (e) The x-component of \(\vec{c}\) - (f) The y-component of \(\vec{c}\) - (g) The value of \(p\) such that \(\vec{c} = p\vec{a} + q\vec{b}\) - (h) The value of \(q\) such that \(\vec{c} = p\vec{a} + q\vec{b}\) ### Diagram Explanation The diagram provided shows a coordinate system with vectors \(\vec{a}\), \(\vec{b}\), and \(\vec{c}\). Vector \(\vec{a}\) is represented with both an x and y component, forming an angle \(\theta\) with the positive x-axis. ### Solution Steps 1. **Calculate the components of \(\vec{a}\):** - \(a_x = a \cos(\theta)\) - \(a_y = a \sin(\theta)\) 2. **Calculate the components of \(\vec{b}\):** - Since no angle is provided for \(\vec{b}\), we assume \(\vec{b}\) lies along a principal axis and will determine its components accordingly. 3. **Determine the combination of \(\vec{a}\) and \(\vec{b}\
Transcribed Image Text:**Vector Components and Combinations: A Guide** The problem here involves three vectors with specific magnitudes and angles, and we need to determine their components in the x and y directions as well as their combinations. The given information: - Vector \(\vec{a}\) has a magnitude \(a = 2.60 \text{ m}\) - Vector \(\vec{b}\) has a magnitude \(b = 2.80 \text{ m}\) - Vector \(\vec{c}\) has a magnitude \(c = 10.1 \text{ m}\) - The angle between vector \(\vec{a}\) and the x-axis is \(\theta = 31.0^\circ\) The goal is to find the following: - (a) The x-component of \(\vec{a}\) - (b) The y-component of \(\vec{a}\) - (c) The x-component of \(\vec{b}\) - (d) The y-component of \(\vec{b}\) - (e) The x-component of \(\vec{c}\) - (f) The y-component of \(\vec{c}\) - (g) The value of \(p\) such that \(\vec{c} = p\vec{a} + q\vec{b}\) - (h) The value of \(q\) such that \(\vec{c} = p\vec{a} + q\vec{b}\) ### Diagram Explanation The diagram provided shows a coordinate system with vectors \(\vec{a}\), \(\vec{b}\), and \(\vec{c}\). Vector \(\vec{a}\) is represented with both an x and y component, forming an angle \(\theta\) with the positive x-axis. ### Solution Steps 1. **Calculate the components of \(\vec{a}\):** - \(a_x = a \cos(\theta)\) - \(a_y = a \sin(\theta)\) 2. **Calculate the components of \(\vec{b}\):** - Since no angle is provided for \(\vec{b}\), we assume \(\vec{b}\) lies along a principal axis and will determine its components accordingly. 3. **Determine the combination of \(\vec{a}\) and \(\vec{b}\
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