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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Question
![### Find Vectors and Perform Vector Operations in \( \mathbb{R}^3 \)
Given the points \( A: (3, -2, 2) \) and \( B: (5, 2, 6) \), find the vector \( \vec{u} = \overrightarrow{AB} \).
\[ \vec{u} = \]
#### Explanation:
To find the vector \( \overrightarrow{AB} \), subtract the coordinates of point \( A \) from point \( B \).
- \( \overrightarrow{AB} = (x_2 - x_1, y_2 - y_1, z_2 - z_1) \)
- Calculate the component-wise differences:
- \( x \)-component: \( 5 - 3 = 2 \)
- \( y \)-component: \( 2 - (-2) = 4 \)
- \( z \)-component: \( 6 - 2 = 4 \)
Therefore, the vector \( \vec{u} = \overrightarrow{AB} = (2, 4, 4) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F55a44e3d-6d6a-4ecd-9343-ab7bc7f808c7%2F2ed9d82d-f51b-482c-81a6-7ccc5b61a270%2F5ck04g_processed.png&w=3840&q=75)
Transcribed Image Text:### Find Vectors and Perform Vector Operations in \( \mathbb{R}^3 \)
Given the points \( A: (3, -2, 2) \) and \( B: (5, 2, 6) \), find the vector \( \vec{u} = \overrightarrow{AB} \).
\[ \vec{u} = \]
#### Explanation:
To find the vector \( \overrightarrow{AB} \), subtract the coordinates of point \( A \) from point \( B \).
- \( \overrightarrow{AB} = (x_2 - x_1, y_2 - y_1, z_2 - z_1) \)
- Calculate the component-wise differences:
- \( x \)-component: \( 5 - 3 = 2 \)
- \( y \)-component: \( 2 - (-2) = 4 \)
- \( z \)-component: \( 6 - 2 = 4 \)
Therefore, the vector \( \vec{u} = \overrightarrow{AB} = (2, 4, 4) \).
Expert Solution
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The points are given by
To evaluate: The vector .
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