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Linear Algebra

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Vector Distance: Between A Scalar Multiple and Vector Sum

LINALG-JJENYS

If $\boldsymbol{u} = \begin{bmatrix} -1\\\ 0\\\ -3\end{bmatrix}$, $\boldsymbol{v} = \begin{bmatrix} -2\\\ 1\\\ -1\end{bmatrix}$, and $\boldsymbol{w} = \begin{bmatrix} 0\\\ -5\\\ 3\end{bmatrix}$, then compute the distance between $2\boldsymbol{u}$ and $\boldsymbol{v}+\boldsymbol{w}$.

A

$5\sqrt{3}$

B

$4\sqrt{5}$

C

$4$

D

$\sqrt{6}$

E

$8$

F

$3\sqrt{10}$