Find v v j 10i - 24
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Question
![**Transcription:**
Find \(|\mathbf{v}|\).
\(\mathbf{v} = 10\mathbf{i} - 24\mathbf{j}\)
---
**Explanation:**
The above text is an exercise asking to find the magnitude of the vector \(\mathbf{v}\). The vector is given in terms of its components along the \(i\) (horizontal) and \(j\) (vertical) directions. The vector \(\mathbf{v}\) is expressed as \(10\mathbf{i} - 24\mathbf{j}\).
To find the magnitude \(|\mathbf{v}|\), use the formula for the magnitude of a vector in two dimensions:
\[
|\mathbf{v}| = \sqrt{(a^2 + b^2)}
\]
where \(a\) and \(b\) are the coefficients of \(\mathbf{i}\) and \(\mathbf{j}\), respectively. In this case, \(a = 10\) and \(b = -24\).
Therefore, the calculation will be:
\[
|\mathbf{v}| = \sqrt{(10^2 + (-24)^2)}
\]
This exercise helps in understanding how to calculate the magnitude of a vector using its components.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb48d2c1d-e6bb-45e6-b6d7-f9e59d1357b7%2Fd3be864c-b1f8-451d-b6d1-f5ae03558cb9%2Fvz44me_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription:**
Find \(|\mathbf{v}|\).
\(\mathbf{v} = 10\mathbf{i} - 24\mathbf{j}\)
---
**Explanation:**
The above text is an exercise asking to find the magnitude of the vector \(\mathbf{v}\). The vector is given in terms of its components along the \(i\) (horizontal) and \(j\) (vertical) directions. The vector \(\mathbf{v}\) is expressed as \(10\mathbf{i} - 24\mathbf{j}\).
To find the magnitude \(|\mathbf{v}|\), use the formula for the magnitude of a vector in two dimensions:
\[
|\mathbf{v}| = \sqrt{(a^2 + b^2)}
\]
where \(a\) and \(b\) are the coefficients of \(\mathbf{i}\) and \(\mathbf{j}\), respectively. In this case, \(a = 10\) and \(b = -24\).
Therefore, the calculation will be:
\[
|\mathbf{v}| = \sqrt{(10^2 + (-24)^2)}
\]
This exercise helps in understanding how to calculate the magnitude of a vector using its components.
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