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Linear Algebra

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Moderate

Vector Distance: Between Scalar Multiples Involving Dot Products

LINALG-ZERJN4

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

A

$2\sqrt{5}$

B

$\sqrt{15}$

C

$\sqrt{14}$

D

$5$

E

$\sqrt{10}$

F

$\sqrt{23}$