Question

The equation of plane passing through point (1, – 1, 2) and vector r = (1, 1, 1) + k(2, 1, 2), k ∈ R is ____

(A) 5x – 2y – 4z + 1 = 0

(B) 5x + 2y + 4z + 1 = 0

(C) 5x – 2y + 4z + 1 = 0

(D) 5x – 2y + 4z = 1   

Answer 1

The correct option (A) 5x – 2y – 4z + 1 = 0

Explanation:

vector r = (1, 1, 1) + k(2, 1, 2) and vector a = (1, 1, 1)

also vector ℓ = (2, 1, 2)

point given b = (1, – 1, 2)

Now vector AB = vector b – vector a = (0, – 2, 1)

Normal of plane

vector n = vector AB x l

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

∴ (x, y, z) ∙ (– 5, 2, 4) = (1, 1, 1) ∙ (– 5, 2, 4)

∴ – 5x + 2y + 4z = – 5 + 2 + 4

∴ 5x – 2y – 4z + 1 = 0.