Vectors in a plane I have a question where i need to prove that three vectors are all on one plane.
I proved that the angle between ALL the three vectors is 120. 
Is that enough to prove that it is on one plane? because together they are 360.
Basiclly, is there any other way to build three vectors with 120 angle between them, without being all on one plane
Thanks!

Assume WLOG that all the vectors are normalized. Then
$$u\cdot v=v\cdot w=u\cdot w=-\frac12$$
Now, consider the equation
$$au+bv+cu\times v=w$$
and dot-product with $u$:
$$a-\frac b2=-\frac12$$
now with $v$:
$$-\frac a2+b=-\frac12$$
and we get $a=b=-1$. Then
$$-u-v+cu\times v=w$$
and dot-product with $w$:
$$\frac12+\frac12+c[u,v,w]=1$$
so $c=0$ or $[u,v,w]=0$, and both facts tell us the same: $u$, $v$ and $w$ are coplanar.
