8. 48. Three vectors A, B, and C have the following x and y components: A: = 1 m, A, = 0 m, B: = 1 m, B, = 1 m, &=0m, C, =-1 m According to the graph, how are A, B , and C combined to result in the vector D? (SectionDef: Section 1-5 and 1-6) %3D D А) D - A - B -с B) D B + C
8. 48. Three vectors A, B, and C have the following x and y components: A: = 1 m, A, = 0 m, B: = 1 m, B, = 1 m, &=0m, C, =-1 m According to the graph, how are A, B , and C combined to result in the vector D? (SectionDef: Section 1-5 and 1-6) %3D D А) D - A - B -с B) D B + C
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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Transcribed Image Text:**Vector Addition and Resultant Vector**
**Question:**
Three vectors **A**, **B**, and **C** have the following \( x \) and \( y \) components:
- \( A_x = 1 \, m \)
- \( A_y = 0 \, m \)
- \( B_x = 1 \, m \)
- \( B_y = 1 \, m \)
- \( C_x = 0 \, m \)
- \( C_y = -1 \, m \)
According to the graph, how are **A**, **B**, and **C** combined to result in the vector **D**?
**Diagram Description:**
The diagram shows a vector **D** represented by an arrow pointing diagonally upward and to the right. There are components or additional vectors shown, breaking down or summarizing the resultant vector **D**.
**Answer Choices:**
A) \( \vec{D} = \vec{A} - \vec{B} - \vec{C} \)
B) \( \vec{D} = \vec{A} - \vec{B} + \vec{C} \)
C) \( \vec{D} = \vec{A} + \vec{B} + \vec{C} \)
D) \( \vec{D} = \vec{A} + \vec{B} - \vec{C} \)
E) \( \vec{D} = -\vec{A} + \vec{B} + \vec{C} \)
**Explanation:**
To better understand how the vectors combine, let’s analyze their components.
1. **Vector \( \vec{A} \)**:
- \( A_x = 1 \)
- \( A_y = 0 \)
- Therefore, \( \vec{A} \) has components \( (1, 0) \).
2. **Vector \( \vec{B} \)**:
- \( B_x = 1 \)
- \( B_y = 1 \)
- Therefore, \( \vec{B} \) has components \( (1, 1) \).
3. **Vector \( \vec{C} \)**:
- \( C_x = 0 \)
- \( C_y = -1 \)
- Therefore, \( \vec{
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