The correct option (C) x + 2y + 4z = 35
Explanation:
plane: 2x + 4y + 8z = 17 ⇒ n = (2, 4, 8) and d = 17
line: [(x – 3)/2] = y = [(z – 8)/(– 1)] ⇒ vector a = (3, 0, 8) and vector ℓ = (2, 1, – 1)
Direction of line vector ℓ = (2, 1, – 1)
vector ℓ ∙ n = (2, 1, – 1) ∙ (2, 4, 8) = 4 + 4 – 8 = 0
point on line does not satisfy the equation of plane
∴ line is parallel to plane.
Let equation of plane parallel to 2x + 4y + 8z = 17 is 2x + 4y + 8z = k.
point on line p(3 + 2t, t, 8 – t) satisfies plane 2x + 4y + 8z = k
∴ 2(3 + 2t) + 4t + 8(8 – t) = k
∴ 6 + 4t + 4t + 64 – 8t = k
∴ k = 70
equation of plane is 2x + 4y + 8z = 70
i.e. x + 2y + 4y = 35.