Verify that the three points with position vectors u, v, and w lie in the plane:

r.(u x v + v x w + w x u) = [u, v, w]

Question

Verify that the three points with position vectors u, v, and w lie in the plane:

r.(u x v + v x w + w x u) = [u, v, w]

jamesj · Answer

What's your definition of [u, v, w] ?

anonymous · Answer

I believe it is referring to the scalar triple product. So u . (v x w)

jamesj · Answer

Then isn't this trivial?  Substitute r = u, v, w in turn and show that the equation is satisfied.

For example, if r = u,
     r.(u x v + v x w + w x u)
=  u.u x v + u.v x w + u.w x u
= 0           + [u,v,w]  + 0

Now try r = v and r = w

anonymous · Answer

Oh, is that all they're asking for? I guess I just didn't understand the question in the first place :/

jamesj · Answer

...and you need to know that [u,v,w] = [v,w,u] = [w,u,v] = -[u,w,v] = -[w,v,u] = -[v,u,w]