The correct option (C) 7x – 2y – 2z + 3 = 0
Explanation:
L: [(x – 1)/2] = [(y – 2)/3] = [(z – 3)/4] ⇒ vector a = (1, 2, 3) and vector ℓ = (2, 3, 4)
also M: [(x – 1) / 2] = (y/3) = [(z – 5)/4] ⇒ vector b = (1, 0, 5) and vector m = (2, 3, 4)
vector ℓ = vector m
⇒ vector ℓ × vector m = 0 i.e. parallel lines
equation of plane is (vector r – vector b) ∙ [vector (b – a) × vector ℓ] = 0 and vector b – vector a = (0, – 2, 2)
∴ (x – 1)[– 8 – 6] – y [0 – 4] + (z – 5)(0 + 4) = 0
∴ – 14(x – 1) + 4y + 4z – 20 = 0
∴ – 14x + 4y + 4z – 6 = 0
∴ – 7x + 2y + 2z – 3 = 0
⇒ 7x – 2y – 2z + 3 = 0.
