The foot of the perpendicular drawn from a point A (1,1,1) on to a plane is P(-3,3,5) . If the equation of the plane parallel to the plane and passing through the midpoint of AP is a x-y+c z+d=0 , then a+c-d=

Step-by-step solution

Since, the foot of the perpendicular to the plane is P (-3,3,5) . Therefore, P (-3,3,5) lies on . Also, direction ratios of the perpendicular line AP is (-4,2,4) . So, equation of is aligned & -4(x+3)+2(y-3)+4(2-5)=0 & -4 x+2 y+4 z-38=0 aligned Also, mid point of A P is (-1,2,3) . Equation of plane parallel to is 4 x-2 y-4 z+ =0 ...(i) It passes through (-1,2,3) =20 Equation (i) becomes, 4 x-2 y-4 z+20=0 2 x-y-2 z+10=0 Comparing with a x-y+c z+d=0a=2, c=-2, d=10 a+c-d=-10