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Linear Algebra

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Vector Normalization: Normalization in 3 Dimensions

LINALG-R0NTB5

Compute the normalization of $\boldsymbol{v} = \begin{bmatrix} 2 \\\ -1/\sqrt{2} \\\ 3/\sqrt{2} \end{bmatrix}$. Remember that the normalization of $\boldsymbol{v}$ is the unit vector pointing in the same direction as $\boldsymbol{v}$.

A

$\begin{bmatrix} 2/3 \\\ -1/3\sqrt{2} \\\ 1/\sqrt{2} \end{bmatrix}$

B

$\begin{bmatrix} 1/\sqrt{6} \\\ -1/2\sqrt{6} \\\ \sqrt{3}/2\sqrt{2} \end{bmatrix}$

C

$\begin{bmatrix} 1/6 \\\ -1/12 \\\ 3/8 \end{bmatrix}$

D

$\begin{bmatrix} \sqrt{2}/6 \\\ -1/6\sqrt{2}\\\ 1/\sqrt{2} \end{bmatrix}$

E

$\begin{bmatrix} 1/\sqrt{2} \\\ -\sqrt{2} \\\ \sqrt{2}/3 \end{bmatrix}$

F

$\begin{bmatrix} 1/\sqrt{2} \\\ -1/\sqrt{2} \\\ \sqrt{2}/3 \end{bmatrix}$

G

$\begin{bmatrix} 1/6\sqrt{2} \\\ -1/6\sqrt{2} \\\ \sqrt{2}/18 \end{bmatrix}$