Calc 3: Proof of coplanar vectors

[Aerith's Knight]

Dammit, you're right.

The proof of this part of the theorem is actually one of the problems at the end of the section in the book. It's an odd question, so the answer is in the back of the book. The question goes:

"Suppose that points P, A, B and C all lie on the same plane. Show that vectors a=PA, b=PB and c=PC are coplanar vectors."

And the only thing the back of the book says for this answer is

"a dot (b x c) = 0"

I looked up the book online, and it gives the answer to all questions in the book in more detail than in the back of the book. And still, for this question all it says is

"a dot (b x c) = 0"

Is it really simple enough to just say that because the points all lie on the same plane, then PA dot (PB x PC) = 0, so a, b and c are all on one plane and thus coplanar?

I think it's supposed to be an insight question. They can only be in the same plane when their volume is zero, which brings it down to that equation.

I don't think you're supposed to derive it, but that it derives itself from the situation. Because I found the same lack of explination in my notes, and if it was an important theorem, I would've gotten it, seeing as my teacher loved to teach us abstract things we don't care about.