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Linear Algebra

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Distance and Vector Subtraction

LINALG-JNLBPN

Suppose $\vec v, \vec w$ are vectors in $\mathbb{R}^n$ with endpoints $P,Q$ respectively, and suppose that $\lVert v\rVert=5$, $\lVert w\rVert=6$, and $\lVert v-w\rVert=10$.

What is the distance between the points $P$ and $Q$?

A

$5$

B

$6$

C

$10$

D

$11$

E

$12$