Step 1:

The points on the plane are .

The points are lies on the plane then their vectors are lies on the same plane.

If are the two points then the component form of vector  is

If are the two points then the component form  of vector  is

Consider .

.

From geometric properties of the cross product, is perpendicular to both .

Then is perpendicular to plane passing through the points .

Solution :

is a non-zero vector perpendicular to plane passing through the points .