Question

Find the equation of the plane that bisects the line joining $(1,2,3)$ and $(3,4,5)$ and is at right angle to the line.

Answer 1

Let $(x,y,z)$ be any point on the plane other than the midpoint of the $(1,2,3),(3,4,5)⟹(2,3,4)$.

$(3-1)(x-2)+(4-2)(y-3)+(5-3)(z-4)=0⟹x+y+z=9$