Vectors and the Menelaus Theorem

[ronblack2003]

Given 3 Non-zero vectors A, B and C in 3-dimensional space which are
non-coplanar. It is easy to show that there exists real constants m,p and n such that (A+mB),(B+pC) and (C+nA) are Co-planar implying mnp=-1.
It seems to me that there should be a natural way of using this result
to easily prove the direct Theorem of Menelaus can anyone help?

 

[Tzar]

I have never heard of that theorm! What is it?

 

[HallsofIvy]

http://www.ies.co.jp/math/java/vector/menela/menela.html