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Linear Algebra

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Vector Normalization: Finding Vectors with a Given Normalization

LINALG-KWYWLH

Which of the following vectors have $\begin{bmatrix} 2/3 \\\ -2/3 \\\ 1/3 \end{bmatrix}$ as its normalization?

Remember that the normalization of a vector $\boldsymbol{v}$ is the unit vector pointing in the same direction as $\boldsymbol{v}$.

A

$\begin{bmatrix} 2 \\\ -2 \\\ 1 \end{bmatrix}$

B

$\begin{bmatrix} -4/3 \\\ 4/3 \\\ -2/3 \end{bmatrix}$

C

$\begin{bmatrix} 4/3 \\\ 4/3 \\\ 2/3 \end{bmatrix}$

D

$\begin{bmatrix} 2 \\\ 2 \\\ -1 \end{bmatrix}$

E

$\begin{bmatrix} 4 \\\ -4 \\\ 2 \end{bmatrix}$

F

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