El find the orthogonal projection of x- > and Subspace of 1² Spanned by IR (a) find 2 2 1 the angle between v IN Not -2 19 onto the 0 9006 to and
El find the orthogonal projection of x- > and Subspace of 1² Spanned by IR (a) find 2 2 1 the angle between v IN Not -2 19 onto the 0 9006 to and
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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Please answer both questions clearly I would like to understand
![**Problem C: Orthogonal Projection**
Find the orthogonal projection of the vector
\[
x = \begin{bmatrix} 9 \\ 0 \\ 0 \end{bmatrix}
\]
onto the subspace of \(\mathbb{R}^3\) spanned by the vectors
\[
\begin{bmatrix} 2 \\ 2 \\ 1 \end{bmatrix}
\]
and
\[
\begin{bmatrix} -2 \\ 2 \\ 0 \end{bmatrix}
\]
---
**Problem D: Angle Between Vectors**
Find the angle between the vectors \( v \)
\[
\begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}
\]
and
\[
\begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8cf9958e-dd38-41eb-b691-55a1e2252bf8%2Fe7a53fef-806c-4cf4-961e-db988c3c8fbf%2F4k13coj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem C: Orthogonal Projection**
Find the orthogonal projection of the vector
\[
x = \begin{bmatrix} 9 \\ 0 \\ 0 \end{bmatrix}
\]
onto the subspace of \(\mathbb{R}^3\) spanned by the vectors
\[
\begin{bmatrix} 2 \\ 2 \\ 1 \end{bmatrix}
\]
and
\[
\begin{bmatrix} -2 \\ 2 \\ 0 \end{bmatrix}
\]
---
**Problem D: Angle Between Vectors**
Find the angle between the vectors \( v \)
\[
\begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}
\]
and
\[
\begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}
\]
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