The vector equation of a plane is a relation satisfied by position vectors of all the points on the plane. If P is a plane and n^ is a unit vector through origin which is perpendicular to the plane P then vector equation of the plane must be r⋅n^=d where d represents perpendicular distance of plane P from origin.
If A is a point vector a then perpendicular distance of A from the plane r⋅n^=d must be
(1) ∣d+a⋅n^∣
(2) ∣d−a⋅n^∣
(3) ∣a∣−d
(4) ∣d−a∣