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Linear Algebra

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Orthogonal Projection of a Vector Onto a Plane

LINALG-ZLOBNV

Which of the following vectors $v$ is the orthogonal projection of $u=\begin{bmatrix}0\\\ \frac{-2}{5} \\\ 1\end{bmatrix}$ onto the plane spanned by:

$$\{u_1, u_2\}=\Bigg\{ \frac{1}{\sqrt{6}}\begin{bmatrix}-2\\\ 1 \\\ 1\end{bmatrix}, \frac{1}{\sqrt{5}}\begin{bmatrix}1 \\\ 0 \\\ 2\end{bmatrix}\Bigg\}$$

A

$v=\begin{bmatrix}0\\\ \frac{-2}{5} \\\ 1\end{bmatrix}$

B

$v=\begin{bmatrix}0\\\ 0 \\\ 0\end{bmatrix}$

C

$v=\frac{1}{10}\begin{bmatrix}2\\\ 1 \\\ 9\end{bmatrix}$

D

$v=\begin{bmatrix}1\\\ 1 \\\ 1\end{bmatrix}$