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# Vector Distance: Involving Dot Products and Linear Combinations

LINALG-JEUE3N

If $\boldsymbol{u} = \begin{bmatrix} 1\\\ -2\\\ 1\end{bmatrix}$, $\boldsymbol{v} = \begin{bmatrix} 0\\\ -5\\\ 3\end{bmatrix}$, $\boldsymbol{w} = \begin{bmatrix} -1\\\ -1\\\ 3\end{bmatrix}$, $\boldsymbol{x} = \begin{bmatrix} 3\\\ -1\\\ -2\end{bmatrix}$, and $\boldsymbol{y} = \begin{bmatrix} -1\\\ 0\\\ -3\end{bmatrix}$

...then compute the distance between $(\boldsymbol{u} \cdot \boldsymbol{v})\boldsymbol{w}$ and $2\boldsymbol{x} - 3\boldsymbol{y}$

A

$4\sqrt{110}$

B

$\sqrt{1761}$

C

$\sqrt{1762}$

D

$\sqrt{1763}$

E

$42$

F

$\sqrt{1765}$