**Problem Statement:**The components of a vector \( \mathbf{A} \) are \( A_X = 2.9 \) and \( A_Y = 5.3 \), and the components of a vector \( \mathbf{B} \) are given as \( B_X = 7.7 \) and \( B_Y = -10 \). What is the magnitude of the vector \( \mathbf{A} + \mathbf{B} \)?**Answer Choices:**- a. 12- b. 11- c. 13- d. 10- e. 9**Solution Explanation:**To find the magnitude of the vector \( \mathbf{A} + \mathbf{B} \), we first need to determine the components of this resultant vector. Given:\[ A_X = 2.9, \quad A_Y = 5.3 \]\[ B_X = 7.7, \quad B_Y = -10 \]The resultant vector \( \mathbf{R} = \mathbf{A} + \mathbf{B} \) will have components:\[ R_X = A_X + B_X = 2.9 + 7.7 = 10.6 \]\[ R_Y = A_Y + B_Y = 5.3 + (-10) = -4.7 \]Now, to find the magnitude of the resultant vector \( \mathbf{R} \):\[ \| \mathbf{R} \| = \sqrt{R_X^2 + R_Y^2} = \sqrt{10.6^2 + (-4.7)^2} \]\[ \| \mathbf{R} \| = \sqrt{112.36 + 22.09} = \sqrt{134.45} \]\[ \| \mathbf{R} \| \approx 11.6 \]Therefore, the closest answer choice provided is:\[ \boxed{11} \]

Given data: Vector A=Ax+Ay ⇒ A=2.9 x + 5.3 y (1) Vector B=Bx+By ⇒ B=7.7 x -10 y…

Answered: The components of a vector are Ax = 2.9…

The components of a vector are Ax = 2.9 and Ay = 5.3, and the components of a vector are given are Bx = 7.7 and By of the vector + ? = -10. What is the magnitude a. 12 b. 11 C. 13 d. 10 e. g

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter3: Vectors

Section: Chapter Questions

Problem 33PQ

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Concept explainers

Scalars and Vectors

Scalars and Vectors are the classification of physical quantities that are used to denote various terms in physics.

Question

**Problem Statement:**

The components of a vector \( \mathbf{A} \) are \( A_X = 2.9 \) and \( A_Y = 5.3 \), and the components of a vector \( \mathbf{B} \) are given as \( B_X = 7.7 \) and \( B_Y = -10 \). What is the magnitude of the vector \( \mathbf{A} + \mathbf{B} \)?

**Answer Choices:**

- a. 12
- b. 11
- c. 13
- d. 10
- e. 9

**Solution Explanation:**

To find the magnitude of the vector \( \mathbf{A} + \mathbf{B} \), we first need to determine the components of this resultant vector.

Given:

\[ A_X = 2.9, \quad A_Y = 5.3 \]
\[ B_X = 7.7, \quad B_Y = -10 \]

The resultant vector \( \mathbf{R} = \mathbf{A} + \mathbf{B} \) will have components:

\[ R_X = A_X + B_X = 2.9 + 7.7 = 10.6 \]
\[ R_Y = A_Y + B_Y = 5.3 + (-10) = -4.7 \]

Now, to find the magnitude of the resultant vector \( \mathbf{R} \):

\[ \| \mathbf{R} \| = \sqrt{R_X^2 + R_Y^2} = \sqrt{10.6^2 + (-4.7)^2} \]
\[ \| \mathbf{R} \| = \sqrt{112.36 + 22.09} = \sqrt{134.45} \]
\[ \| \mathbf{R} \| \approx 11.6 \]

Therefore, the closest answer choice provided is:

\[ \boxed{11} \]

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