Question

Line [(x – α)/ℓ] = [(y – β)/m] = [(z – γ)/n] and [(x – ℓ) / α] = [(y – m)/β] = [(z – n)/γ] is ____

(A) intersecting

(B) parallel 

(C) non coplanar

(D) perpendicular   

Answer 1

The correct option (A) intersecting   

Explanation:

 line:   [(x – α)/ℓ] = [(y – β)/m] = [(z – γ)/n] and 

[(x – ℓ)/α] = [(y – m)/β] = [(z – n)/γ]

lines:   vector r = (α, β, γ) + k(ℓ, m, n) and vector r = (ℓ, m, n) + k(α, β, γ)

∴ vector a = (α, β, γ), vector ℓ = (ℓ, m, n) also vector b = (ℓ, m, n) and vector m = (α, β, γ)

Now vector(l x m)

   vector AB = vector(b – a) = (ℓ – α, m – β, n – γ)

∴ vector AB ∙ vector(ℓ × m)

 ⇒ line are intersecting.