Linear Algebra

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Vector Distance: Distance with Scalar Multiplication

LINALG-EY3ZLB

If $\boldsymbol{u} = \begin{bmatrix} 7\\\ 0\\\ 1\end{bmatrix}$ and $\boldsymbol{v} = \begin{bmatrix} 6\\\ 1\\\ 1\end{bmatrix}$, then compute the distance between $-\dfrac{1}{2}\boldsymbol{u}$ and $\dfrac{1}{3}\boldsymbol{v}$.

A

$\sqrt{30}$

B

$\dfrac{\sqrt{123}}{2}$

C

$\dfrac{5\sqrt{11}}{3}$

D

$\dfrac{4\sqrt{17}}{3}$

E

$\dfrac{11\sqrt{10}}{6}$

F

$\dfrac{\sqrt{1118}}{6}$