Plane through three points

Determine the plane through A(2, 6, 10), B(24, 5, 8) and C(20, 8, 14). State whether the three points are collinear.

Step-by-step solution

Two pairs of points give two lines of the plane: AB and AC.
The plane normal is the cross product of those two directions.
If the cross product is zero, the points are collinear and do not define a plane.
Check that all three points satisfy the plane equation.

Result: α: −124y + 62z + 124 = 0.

Three collinear points do not define a plane: it is the case to check before drawing.