Show that the four points `A ,B , Ca n dD` with position vectors ` vec a , vec b , vec c` and ` vec d` respectively are coplanar if and only if `3 vec a-2 vec b+ vec c-2 vec d=0.`

Explanation

Position vectors, `veca,vecb,vecc and vec d` are coplanar if,

`xveca+yvecb+zvecc+wvecd = vec0->(1)`

and

`x+y+z+w = 0`

If we put, ` x = 3, y = -2, z = 1 and w = -2`,

Then, `x+y+z+w = 0`

If we put these values in (1),

`3veca-2vecb+vecc-2vecd = vec0.`

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