14. The components of two vectors A and B are given as 4, = 3, 4, = -4, B. =-3, B, = 3. If C = A + B, what is the magnitude of the vector C? 24 A) 0 B) -1 +1D) -7 E none of the above JAX √√/13)² + (-4) √(3-4)=57
14. The components of two vectors A and B are given as 4, = 3, 4, = -4, B. =-3, B, = 3. If C = A + B, what is the magnitude of the vector C? 24 A) 0 B) -1 +1D) -7 E none of the above JAX √√/13)² + (-4) √(3-4)=57
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 Addition Problem**
**Problem Statement:**
The components of two vectors \( \mathbf{A} \) and \( \mathbf{B} \) are given as \( A_x = 3 \), \( A_y = -4 \), \( B_x = -3 \), \( B_y = 3 \). If \( \mathbf{C} = \mathbf{A} + \mathbf{B} \), what is the magnitude of the vector \( \mathbf{C} \)?
**Options:**
A) 0
B) -1
C) +1
D) -7
E) none of the above
_Correct Answer: B) -1_
**Solution Explanation:**
To solve for the magnitude of vector \( \mathbf{C} \), calculate the components of \( \mathbf{C} \) first:
\[
C_x = A_x + B_x = 3 + (-3) = 0
\]
\[
C_y = A_y + B_y = -4 + 3 = -1
\]
Next, the magnitude of vector \( \mathbf{C} \) is calculated using the formula for the magnitude of a vector:
\[
|\mathbf{C}| = \sqrt{C_x^2 + C_y^2}
\]
\[
|\mathbf{C}| = \sqrt{0^2 + (-1)^2} = \sqrt{1} = 1
\]
The answer is 1, so the selected answer from the list is **C) +1**.
**Diagram Explanation:**
The accompanying sketch shows the vector addition process on a Cartesian plane, with each vector represented by arrows:
- \( \mathbf{A} \) is highlighted going from the origin to the point (3, -4).
- \( \mathbf{B} \) is highlighted from the origin to the point (-3, 3).
- The resultant \( \mathbf{C} \) from the vector addition ends at the point (0, -1) and is shown on the coordinate plane.
- The individual squared terms and their sum inside the square root are illustrated to clarify how the magnitude formula applies here.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F38e39407-372d-4edd-bcc1-3a69e099571e%2Fac3ce81a-57c3-4b4f-a7ed-6b17f4f78268%2F5vs1n9t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Vector Addition Problem**
**Problem Statement:**
The components of two vectors \( \mathbf{A} \) and \( \mathbf{B} \) are given as \( A_x = 3 \), \( A_y = -4 \), \( B_x = -3 \), \( B_y = 3 \). If \( \mathbf{C} = \mathbf{A} + \mathbf{B} \), what is the magnitude of the vector \( \mathbf{C} \)?
**Options:**
A) 0
B) -1
C) +1
D) -7
E) none of the above
_Correct Answer: B) -1_
**Solution Explanation:**
To solve for the magnitude of vector \( \mathbf{C} \), calculate the components of \( \mathbf{C} \) first:
\[
C_x = A_x + B_x = 3 + (-3) = 0
\]
\[
C_y = A_y + B_y = -4 + 3 = -1
\]
Next, the magnitude of vector \( \mathbf{C} \) is calculated using the formula for the magnitude of a vector:
\[
|\mathbf{C}| = \sqrt{C_x^2 + C_y^2}
\]
\[
|\mathbf{C}| = \sqrt{0^2 + (-1)^2} = \sqrt{1} = 1
\]
The answer is 1, so the selected answer from the list is **C) +1**.
**Diagram Explanation:**
The accompanying sketch shows the vector addition process on a Cartesian plane, with each vector represented by arrows:
- \( \mathbf{A} \) is highlighted going from the origin to the point (3, -4).
- \( \mathbf{B} \) is highlighted from the origin to the point (-3, 3).
- The resultant \( \mathbf{C} \) from the vector addition ends at the point (0, -1) and is shown on the coordinate plane.
- The individual squared terms and their sum inside the square root are illustrated to clarify how the magnitude formula applies here.
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