Question

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

(A) 2x − y + z = 4

(B) 2x + y + z = 4

(C) x − 3y + z = 5

(D) x − 4y + 2z = 5

Answer 1

Answer is (A) 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 are <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