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# Parallelogram Law and Triangle Sides

LINALG-MDMJZN

Let $\vec v$ and $\vec w$ be vectors in $\mathbb{R}^6$ such that:

$$\lVert v\rVert=2$$
$$\lVert w\rVert=5$$
$$\lVert v+w\rVert=4$$

In the triangle whose vertices are the origin and the endpoints of $\vec v$ and $\vec w$, what is the length of the side opposite the origin?

A

$2$

B

$\sqrt{7}$

C

$4$

D

$\sqrt{29}$

E

$\sqrt{42}$