Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Mathematics Problem: Finding the Length of a Vector**
Given a point \( R = (6, 5) \), we aim to calculate the length of the vector \( \overrightarrow{OR} \).
The notation \( \overrightarrow{OR} \) represents the vector from the origin \( O \) (which is at the coordinates (0,0)) to the point \( R \).
To find the length (or magnitude) of the vector \( \overrightarrow{OR} \), we use the formula:
\[
\| \overrightarrow{OR} \| = \sqrt{x^2 + y^2}
\]
where \( x \) and \( y \) are the coordinates of the point \( R \).
In this case, the coordinates of \( R \) are \( x = 6 \) and \( y = 5 \).
Therefore, substituting these values into the formula:
\[
\| \overrightarrow{OR} \| = \sqrt{6^2 + 5^2} = \sqrt{36 + 25} = \sqrt{61}
\]
So, the length of the vector \( \overrightarrow{OR} \) is \( \sqrt{61} \).
\[
\| \overrightarrow{OR} \| = \boxed{\sqrt{61}}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc6153184-8fe0-4ef7-a5e4-91319420d9fb%2F915c5c43-8017-4521-b58b-e54c9a3c0034%2F0wd1229.png&w=3840&q=75)
Transcribed Image Text:**Mathematics Problem: Finding the Length of a Vector**
Given a point \( R = (6, 5) \), we aim to calculate the length of the vector \( \overrightarrow{OR} \).
The notation \( \overrightarrow{OR} \) represents the vector from the origin \( O \) (which is at the coordinates (0,0)) to the point \( R \).
To find the length (or magnitude) of the vector \( \overrightarrow{OR} \), we use the formula:
\[
\| \overrightarrow{OR} \| = \sqrt{x^2 + y^2}
\]
where \( x \) and \( y \) are the coordinates of the point \( R \).
In this case, the coordinates of \( R \) are \( x = 6 \) and \( y = 5 \).
Therefore, substituting these values into the formula:
\[
\| \overrightarrow{OR} \| = \sqrt{6^2 + 5^2} = \sqrt{36 + 25} = \sqrt{61}
\]
So, the length of the vector \( \overrightarrow{OR} \) is \( \sqrt{61} \).
\[
\| \overrightarrow{OR} \| = \boxed{\sqrt{61}}
\]
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