Question

Let u, v and w be three non-zero vectors no two of which are parallel.

Show that if

u × v = v × w = w × u

then

u + v + w = 0.

Answer 1

lolok at \[(u+v+w) \times u\]
\[(u+v+w) \times v\]
\[(u+v+w) \times w\]

Answer 2

do you see what you need to do?

Answer 3

Yep. Thanks.