A plane is passed through the middle point of the segment A (–2, 5, 1), B (6, 1, 5) and is perpendicular to this line. Its equation is :

2x − y + z = 4

Mid−point of A (− 2, 5, 1) and B (6, 1, 5) is (2, 3, 3) 

direction ratios of the line joining A and B is <2, − 1, 1>

Therefore equation of the line perpendicular to AB and passing through (2, 3, 3) is

2(x – 2) – 1(y – 3) + 1(z – 3) = 0 ⇒ 2x − y + z = 4