Question

Lines  vector r = (1, 2, 6) + k(1, 3, 5) and vector r = (– 1, 3, 5) + k(2, 1, 1), k ∈ R are ____

(A) parallel

(B) Intersecting

(C) coincident

(D) skew

Answer 1

The correct option (D) skew  

Explanation:

vector r = (1, 2, 6) + k(1, 3, 5)

∴ vector a = (1, 2, 6) and vector ℓ = (1, 3, 5)

also vector r = (– 1, 3, 5) + k(2, 1, 1)

∴ vector b = (– 1, 3, 5) and vector m = (2, 1, 1)   

vector l x vector m

∴ lines are intersecting or skew 

vector AB = b – a = (– 2, 1, – 1) 

AB ∙ (ℓ × m) = (– 2, 1, – 1) ∙ (– 2, 9, – 5) = 4 + 9 + 5 = 18 ≠ 0

∴ lines are skew.