Let u = (-3, 1, 7), v = (3,0, -6), and w = (6, -1, –3) Find the components of v – w. (-4, 1, 3) V - W =
Let u = (-3, 1, 7), v = (3,0, -6), and w = (6, -1, –3) Find the components of v – w. (-4, 1, 3) V - W =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Problem Statement:**
Given vectors:
\( \mathbf{u} = (-3, 1, 7) \)
\( \mathbf{v} = (3, 0, -6) \)
\( \mathbf{w} = (6, -1, -3) \)
**Task:**
Find the components of \( \mathbf{v} - \mathbf{w} \).
**Attempt:**
\( \mathbf{v} - \mathbf{w} = (-4, 1, 3) \)
**Feedback:**
Your answer is incorrect.
**Explanation of Incorrect Attempt:**
To find the vector subtraction \( \mathbf{v} - \mathbf{w} \), perform component-wise subtraction:
\[
\mathbf{v} - \mathbf{w} = (v_1 - w_1, v_2 - w_2, v_3 - w_3)
\]
Calculating each component:
- First component: \( 3 - 6 = -3 \)
- Second component: \( 0 - (-1) = 1 \)
- Third component: \( -6 - (-3) = -3 \)
Thus, the correct result should be \( (-3, 1, -3) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F46c0fb16-724b-4726-818c-9156075ac6cc%2Fffb28763-13fe-4d20-a31d-84f9c13f620c%2Fh42us9n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Given vectors:
\( \mathbf{u} = (-3, 1, 7) \)
\( \mathbf{v} = (3, 0, -6) \)
\( \mathbf{w} = (6, -1, -3) \)
**Task:**
Find the components of \( \mathbf{v} - \mathbf{w} \).
**Attempt:**
\( \mathbf{v} - \mathbf{w} = (-4, 1, 3) \)
**Feedback:**
Your answer is incorrect.
**Explanation of Incorrect Attempt:**
To find the vector subtraction \( \mathbf{v} - \mathbf{w} \), perform component-wise subtraction:
\[
\mathbf{v} - \mathbf{w} = (v_1 - w_1, v_2 - w_2, v_3 - w_3)
\]
Calculating each component:
- First component: \( 3 - 6 = -3 \)
- Second component: \( 0 - (-1) = 1 \)
- Third component: \( -6 - (-3) = -3 \)
Thus, the correct result should be \( (-3, 1, -3) \).
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