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## Homework Statement

Show that u, v, w lie in the same plane in R3 if and only if u · (v × w) = 0.

## Homework Equations

## 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?

Thanks!