Given P,Q,R,S in R3
If one of PQ, PR, PS is equal to one of QR, QS, the points determine a parallelogram.
QR=(0,-2,-2), itís a parallelogram
Since QR equals PS, it follows immediateley that QR and RS are adjacent sides of the parallelogram and the area is:
If you change S to (-1,-2,1), the conditions are not met and P,Q.R,S is not a parallelogram
This proof did not show up on an Internet search, which is why I post it here.