Find the equation of a plane, given that the foot of perpendicular drawn to the plane from origin is (2,1,2) .

Step-by-step solution

Given, foot of perpendicular drawn from origin to the plane is (2,1,2) . Equation of plane ( r - a ) n =0 where, a = Position vector of point on the plane n = normal vector Now here, a = PV of A aligned & =2 i + j +2 k n & = O A & = PV of A- PV of O=2 i + j +2 k aligned Equation of plane is aligned ( r - a ) n & =0 r n & = a n r (2 i + j +2 k ) & =(2 i + j +2 k ) (2 i + j +2 k ) r (2 i + j +2 k ) & =4+1+4 r (2 i + j +2 k ) & =9 aligned In cartesian form, equation of plane is 2 x+y+2 z=9