Let x = Find xy. Find ||yl|. 6 1 5 3 and y HOTO -1 be two vectors in R6. Find the distance d(x, y) between the vectors x and y. Find the angle between x and y. (Please give your answer in degrees between 0 and 180.)
Let x = Find xy. Find ||yl|. 6 1 5 3 and y HOTO -1 be two vectors in R6. Find the distance d(x, y) between the vectors x and y. Find the angle between x and y. (Please give your answer in degrees between 0 and 180.)
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
![Let \(\mathbf{x} = \begin{bmatrix} -6 \\ 1 \\ 5 \\ 3 \\ 1 \\ 0 \end{bmatrix}\) and \(\mathbf{y} = \begin{bmatrix} 1 \\ 0 \\ -1 \\ 0 \\ -1 \\ 1 \end{bmatrix}\) be two vectors in \(\mathbb{R}^6\).
1. Find \(\mathbf{x} \cdot \mathbf{y}\).
\[
\begin{bmatrix} -6 \\ 1 \\ 5 \\ 3 \\ 1 \\ 0 \end{bmatrix} \cdot \begin{bmatrix} 1 \\ 0 \\ -1 \\ 0 \\ -1 \\ 1 \end{bmatrix} = \, \_\_\_
\]
2. Find \(\|\mathbf{y}\|\).
\[
\|\begin{bmatrix} 1 \\ 0 \\ -1 \\ 0 \\ -1 \\ 1 \end{bmatrix}\| = \, \_\_\_
\]
3. Find the distance \(d(\mathbf{x}, \mathbf{y})\) between the vectors \(\mathbf{x}\) and \(\mathbf{y}\).
\[
d(\mathbf{x}, \mathbf{y}) = \, \_\_\_
\]
4. Find the angle between \(\mathbf{x}\) and \(\mathbf{y}\). (Please give your answer in degrees between 0 and 180.)
\[
\theta = \, \_\_\_ \text{ degrees}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe354d500-dc10-4e3d-a060-42009e500b8b%2Fa4780af1-ad70-48df-9ddc-193ae01df201%2Fw7bxcw4_processed.png&w=3840&q=75)
Transcribed Image Text:Let \(\mathbf{x} = \begin{bmatrix} -6 \\ 1 \\ 5 \\ 3 \\ 1 \\ 0 \end{bmatrix}\) and \(\mathbf{y} = \begin{bmatrix} 1 \\ 0 \\ -1 \\ 0 \\ -1 \\ 1 \end{bmatrix}\) be two vectors in \(\mathbb{R}^6\).
1. Find \(\mathbf{x} \cdot \mathbf{y}\).
\[
\begin{bmatrix} -6 \\ 1 \\ 5 \\ 3 \\ 1 \\ 0 \end{bmatrix} \cdot \begin{bmatrix} 1 \\ 0 \\ -1 \\ 0 \\ -1 \\ 1 \end{bmatrix} = \, \_\_\_
\]
2. Find \(\|\mathbf{y}\|\).
\[
\|\begin{bmatrix} 1 \\ 0 \\ -1 \\ 0 \\ -1 \\ 1 \end{bmatrix}\| = \, \_\_\_
\]
3. Find the distance \(d(\mathbf{x}, \mathbf{y})\) between the vectors \(\mathbf{x}\) and \(\mathbf{y}\).
\[
d(\mathbf{x}, \mathbf{y}) = \, \_\_\_
\]
4. Find the angle between \(\mathbf{x}\) and \(\mathbf{y}\). (Please give your answer in degrees between 0 and 180.)
\[
\theta = \, \_\_\_ \text{ degrees}
\]
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