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Linear Algebra

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Moderate

Vector Distance: Between Normalized Vectors

LINALG-S3LXJ6

If $\boldsymbol{u} = \begin{bmatrix} 5\\\ 4\\\ 3\end{bmatrix}$ and $\boldsymbol{v} = \begin{bmatrix} 1\\\ 0\\\ -1\end{bmatrix}$, then compute the distance between $\dfrac{1}{\Vert\boldsymbol{u}\Vert}\boldsymbol{u}$ and $\dfrac{1}{\Vert\boldsymbol{v}\Vert}\boldsymbol{v}$.

A

$4\sqrt{3}$

B

$\dfrac{5\sqrt{10}}{2}$

C

$2\sqrt{154}$

D

$\sqrt{2}$

E

$\dfrac{2\sqrt{10}}{5}$

F

$5\sqrt{154}$