Since the plane bisects the line joining the points (1,2,3) and (-3,4,5) then the plane passes through the midpoint of the line which is:
(,,)≡(,,) ≡(−1,3,4) As plane cuts the line segment at right angle, so the direction cosines of the normal of the plane are
(−3−1,4−2,5−3)=(−4,2,2) So the equation of the plane is
:−4x+2y+2z=λ As plane passes through (-1,3,4) so
−4(−1)+2(3)+2(4)=λ ⇒λ=18 Therefore, equation of plane is
:−4x+2y+2z=18 Now, only (-3,2,1) satisfies the given plane as
−4(−3)+2(2)+2(1)=18