to a vector is given by ( or r n a n . Substituting a = in the above equation, we get ( ( ) ( Thus, the required vector equation of the plane is ( . If xi yj zk then we get the Cartesian equation of the plane Example . A variable plane moves in such a way that the sum of the reciprocals of its intercepts on the coordinate axes is a constant.
Show that the plane passes through a fixed point The equation of the plane having intercepts , , a b c on the , , x y z axes respectively is = . Since the sum of the reciprocals of the intercepts on the coordinate axes is a constant, we have , where k is a constant, and which can be written as b k c k This shows that the plane = passes through the fixed point k k k