Question

Find the equation of the plane passing through the point (1, 1, –1) and perpendicular to the planes x + 2y + 3z – 7 = 0 and 2x – 3y + 4z = 0

(A) 17x + 2y – 7z = 26

(B) 17x – 2y + 7z = 26

(C) 17x + 2y – 7z + 26 = 0

(D) 17x – 2y + 7z + 26 = 0

Answer 1

Correct option: (A) 17x + 2y – 7z = 26

Explanation:

Let equation of required plane a(x – 1) + b(y – 1) + c(z + 1) = 0

since it is ⟂r to the planes x + 2y + 3z = 7 & 2x – 3y + 4z = 0

∴ a + 2b + 3c = 0

2a – 3b + 4c = 0

∴ eqaution of plane is 17x + 2y – 7z = 26