Equation of plane through the point (1,1,1) is of the form A (x – 1) + B (y – 1) + C (z – 1) = 0.
This plane containing the line
(x – 1) (4) – (y – 1) (20 – 12) +(z – 1) (4)
4x – 4 – 8y + 8 + 4z – 4 = 0
4x-8y + 4z = 0 ⇒ x -2y + z = 0
since the point (1,-2, -5) lies on the plane
x – 2y + z = 0 as 1 x 1 – 2x – 2 – 5 = 0 and
(i - 2j - 5k).(i - 2j + k) = 1 + 4 - 5 = 0 the plane x - 2y + z = 0 contains the lines