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Equation of plane parallel to 2x + 4y + 8z = 17 containing and line [(x – 3)/2] = y = [(z – 8)/(– 1)] is ____

(A) x – 2y – 48 = 35

(B) x – 2x – 4z = 35

(C) x + 2y + 4z = 35

(D) x + 2y – 4z = 35

1 Answer

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Best answer

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.

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