Show $\langle u,v \rangle = -\frac{1}{2}$ when $u+v+w=0$ and $\|u\|=\|v\|=\|w\|=1$? Show $\langle u,v \rangle = -\frac{1}{2}$ when $u+v+w=0$ and $\|u\|=\|v\|=\|w\|=1$?
My thinking is:
$\langle u+v+w,v \rangle =0 \iff \langle u,v \rangle + \langle w,v \rangle = -1$
How do i continue?

$$\langle w,w\rangle = 1$$
leads to
$$\langle -u-v,-u-v\rangle =1.$$
Expand and simplify and you're done.
