2 -5 Let y = -3 and u = -4 -1 3 Compute the distance d from y to the line through u and the origin. d =
2 -5 Let y = -3 and u = -4 -1 3 Compute the distance d from y to the line through u and the origin. d =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![### Linear Algebra Problem: Distance from a Point to a Line
Given the following vectors:
\[ \mathbf{y} = \begin{bmatrix} 2 \\ -3 \\ -1 \end{bmatrix} \quad \text{and} \quad \mathbf{u} = \begin{bmatrix} -5 \\ -4 \\ 3 \end{bmatrix} \]
Compute the distance \( d \) from \( \mathbf{y} \) to the line through \( \mathbf{u} \) and the origin.
#### What You Need to Do:
1. Find the projection of \( \mathbf{y} \) onto \( \mathbf{u} \).
2. Use the projection to calculate the distance \( d \) between \( \mathbf{y} \) and the line defined by \( \mathbf{u} \) through the origin.
Please enter the computed distance into the box below:
\[ d = \boxed{\phantom{-}} \]
---
### Explanation of Graphs/Diagrams:
There are no graphs or diagrams in this example. It is purely a computational problem involving vector arithmetic.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30a42a85-c58f-45ac-a4af-faeed1a599e1%2F6e6fe1ce-3976-4828-a4c4-910597adaefe%2Fggl6s8_processed.png&w=3840&q=75)
Transcribed Image Text:### Linear Algebra Problem: Distance from a Point to a Line
Given the following vectors:
\[ \mathbf{y} = \begin{bmatrix} 2 \\ -3 \\ -1 \end{bmatrix} \quad \text{and} \quad \mathbf{u} = \begin{bmatrix} -5 \\ -4 \\ 3 \end{bmatrix} \]
Compute the distance \( d \) from \( \mathbf{y} \) to the line through \( \mathbf{u} \) and the origin.
#### What You Need to Do:
1. Find the projection of \( \mathbf{y} \) onto \( \mathbf{u} \).
2. Use the projection to calculate the distance \( d \) between \( \mathbf{y} \) and the line defined by \( \mathbf{u} \) through the origin.
Please enter the computed distance into the box below:
\[ d = \boxed{\phantom{-}} \]
---
### Explanation of Graphs/Diagrams:
There are no graphs or diagrams in this example. It is purely a computational problem involving vector arithmetic.
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