Question

How to prove (or disprove) that points P, Q, R, and S are on the same plane?

Answer 1

Here's my reasoning, please tell me if it's right:
- Assume lines PQ, QR, and RS are all on the plane
- Find PQ cross QR and QR cross RS to get normal lines A and B
- If A and B are parallel, then the points are all on the same plane
Is this correct reasoning? Is there a simpler way to solve?

Answer 2

what's P, Q, R and S?

Answer 3

that will work.

another way :-

\([PQ, PR, PS] = 0\)

=> P, Q, R, S are coplanar

Answer 4

@ganeshie8 I don't understand your notation. Could you explain further?

Answer 5

\([PQ, PR, PA] = 0\)

is same as :-

\((PQ \times PR) . PA = 0\)