Question

The equation of plane passing through (1, 6, – 4) and containing [(x – 1)/2] = [(y – 2)/(– 3)] = [(z – 3)/(– 1)] is          ____

(A) 25x + 14y + 8z = 77

(B) 25x + 14y – 8y = 77

(C) 25x – 14y – 8z = 77

(D) 25x + 14y + 8y = – 77

Answer 1

The correct option (A) 25x + 14y + 8z = 77   

Explanation:

plane A(1, 6, – 4) lie on given line.

Line: [(x – 1)/2] = [(y – 2)/(– 3)] = [(z – 3)/(– 1)] 

⇒ vector a = (1, 2, 3) and 

vector ℓ = (2, – 3, – 1)

also Let A(b) = (1, 6, – 4)

∴ vector AB = b – a = (1, 6, – 4) – (1, 2, 3) = (0, 4, – 7)

Now vector n

equation of plane: vector r ∙ n = vector a ∙ n

∴ (x, y, z) ∙ (– 25, – 14, – 8) = (1, 2, 3)(– 25, – 14, – 8)

∴ – 25x – 14y – 8z = – 25 – 28 – 24 

⇒ 25x + 14y + 8z = 77.