Show that u, v, w lie in the same plane in R3 if and only if u · (v × w) = 0.
The Attempt at a Solution
if u · (v × w) = 0, then u is orthogonal to vxw, and
vxw is orthogonal to v and w.
therefore, u must lie in the same plane determined by v and w (i.e. they are coplanar)
Is this correct? Also, how would i describe this proof mathematically?