The eqn. of a plane through points
#P(x_1,y_1,z_1), Q(x_2,y_2,z_2) and R(x_3,y_3,z_3)# is given by,
#|(x-x_1,y-y_1,z-z_1), (x_2-x_1,y_2-y_1,z_2-z_1),(x_3-x_1,y_3-y_1,z_3-z_1)|=0#.
#:.|(x-5,y+2,z+2),(-5-5,-5+2,-5+2),(-3-5,3+2,2+2)|=0#.
#:. |(x-5,y+2,z+2),(-10,-3,-3),(-8,5,4)|=0#.
#:.(x-5)(-12+15)-(y+2)(-40-24)+(z+2)(-50-24)=0#.
#:. 3(x-5)+64(y+2)-74(z+2)=0#.
#rArr 3x+64y-74z=35#, is the desired eqn. of the plane.