Question

The equation of plane passing through the lines L: [(x + 3)/2] = [(y + 3)/3] = [(z – 7)/(– 3)] and M: [(x + 1)/4] = [(y + 1)/5] = [(z + 1)/(– 1)] is ____

(A) 6x + 5y – z = 0

(B) 6x – 5y – z = 0

(C) 6x – 5y + z = 0

(D) 6x + 5y + z = 0

Answer 1

The correct option (B) 6x – 5y – z = 0

Explanation:

L: [(x + 3)/2] = [(y + 5)/3] = [(z – 7)/(– 3)] ⇒ vector a = (– 3, – 5, 7) and vector ℓ = (2, 3, – 3)

M: [(x + 1)/4] = [(y + 1)/5] = [(z + 1)/(– 1)] ⇒ vector b = (– 1, – 1, – 1) and 

vector m = (4, 5, – 1)

Now (vector b - vector a) . (vector l x vector m)

∴ lines are coplanar

equation of plane vector (r – a) ∙ vector (ℓ × m) = 0

∴ 12x + 36 – 10y – 50 – 2z + 14 = 0

∴ 6x – 5y – z = 0.