3-D geometry : three vertices of a ||gm ABCD is (3,-1,2), (1,2,-4) & (-1,1,2). Find the coordinate of the fourth vertex. The question is

Three vertices of a parallelogram ABCD are A(3,-1,2), B(1,2,-4) and C(-1,1,2). Find the coordinate of the fourth vertex.

To get the answer I tried the distance formula, equated AB=CD and AC=BD.

You don't need to consider distance. You need to compute the difference vectors between adjacent sides. For instance, compute the difference vector from $B$ to $A$ and then add that to $C$.
