Equation of the plane such that foot of altitude drawn from (−1,1,1) to the plane has the  coordinate (3,−2,−1) is

Clearly, the direction ratios of normal to the plane are 4,−3,−2 .   Thus equation of plane will be 4x−3y−2z=d .  It will necessarily pass though (3,−2,−1) ie., d=12+6+2=20 Thus the equation of plane is 4x−3y−2z=20