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

Question

johnt · Answer

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?

kc_kennylau · Answer

what's P, Q, R and S?

ganeshie8 · Answer

that will work. 

another way :-

$[PQ, PR, PS] = 0$  

=>  P, Q, R, S are coplanar

johnt · Answer

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

ganeshie8 · Answer

$[PQ, PR, PA] = 0$

is same as :-

$(PQ \times PR) . PA  = 0$

ganeshie8 · Answer

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