- #1

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We have three arbitrary vectors a,b and c. Then we have another 3 vectors:

x = qc - mb

y = ma - pc

z = pb - qa

and I have to prove that these three vectors are not coplanar.

My idea is that I should use mixed vector product because if vectors are coplanar then they don't form parallelepiped so the result of a mixed vector product which expresses the volume of the parallelepiped is equal to 0.

The other possible option is to try to prove that one vector can be expressed with the other two... but this can be very complicated I think.

What do you think... am I on the right way?