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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![**Vector Problem Example and Solution**
**Problem Statement:**
Let \(\vec{a} = -2\vec{i} + 5\vec{j} + 4\vec{k}\). Find \(|\vec{a}|\).
**Solution:**
To find the magnitude of the vector \(\vec{a}\), we use the formula for the magnitude of a vector in three-dimensional space:
\[ |\vec{a}| = \sqrt{a_x^2 + a_y^2 + a_z^2} \]
Here, \(a_x\), \(a_y\), and \(a_z\) are the components of the vector \(\vec{a}\).
Given \( \vec{a} = -2\vec{i} + 5\vec{j} + 4\vec{k} \), we have:
- \(a_x = -2\)
- \(a_y = 5\)
- \(a_z = 4\)
Now, we can calculate the magnitude:
\[ |\vec{a}| = \sqrt{(-2)^2 + 5^2 + 4^2} \]
\[ |\vec{a}| = \sqrt{4 + 25 + 16} \]
\[ |\vec{a}| = \sqrt{45} \]
\[ |\vec{a}| = 3\sqrt{5} \]
Therefore, the magnitude of \(\vec{a}\) is \( 3\sqrt{5} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F55d3466e-6a31-4aff-972b-e33941523058%2F8da3e3e7-a656-4fa6-8746-5a083c5de09a%2Fdzchzpa_processed.png&w=3840&q=75)
Transcribed Image Text:**Vector Problem Example and Solution**
**Problem Statement:**
Let \(\vec{a} = -2\vec{i} + 5\vec{j} + 4\vec{k}\). Find \(|\vec{a}|\).
**Solution:**
To find the magnitude of the vector \(\vec{a}\), we use the formula for the magnitude of a vector in three-dimensional space:
\[ |\vec{a}| = \sqrt{a_x^2 + a_y^2 + a_z^2} \]
Here, \(a_x\), \(a_y\), and \(a_z\) are the components of the vector \(\vec{a}\).
Given \( \vec{a} = -2\vec{i} + 5\vec{j} + 4\vec{k} \), we have:
- \(a_x = -2\)
- \(a_y = 5\)
- \(a_z = 4\)
Now, we can calculate the magnitude:
\[ |\vec{a}| = \sqrt{(-2)^2 + 5^2 + 4^2} \]
\[ |\vec{a}| = \sqrt{4 + 25 + 16} \]
\[ |\vec{a}| = \sqrt{45} \]
\[ |\vec{a}| = 3\sqrt{5} \]
Therefore, the magnitude of \(\vec{a}\) is \( 3\sqrt{5} \).
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