The points 𝐴(3,−1 ,2) ,𝐵(1 ,2 ,−4 ) and 𝐶 (−1 ,1 ,−2 ) are three vertices of a parallelogram ABCD.
(i) Show that the vector 𝑟 = −16𝑗 – 8𝑘 is perpendicular to the plan through 𝐴 ,𝐵 and 𝐶 .
(6 marks)
(ii) Find the cartesian equation of the plane through 𝐴 ,𝐵 and 𝐶 . (4 marks)