If lines (x - 2)/a1 = (y - 3)/b1 = z/c1 and (x - a2)/α = (y - b2)/β = (z - c2)/γ

Question

If lines \(\frac{x - 2}{a_1} = \frac{y - 3}{b_1} = \frac{z}{c_1}\) and \(\frac{x - a_2}{\alpha} = \frac{y - b_2}{\beta} = \frac{z - c_2}{\gamma}\) are parallel then

(x - 2)/a₁ = (y - 3)/b₁ = z/c₁ and (x - a₂)/α = (y - b₂)/β = (z - c₂)/γ

(A) \(\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}\)

(B) \(\frac{a_1}{\alpha} = \frac{b_1}{\beta} = \frac{c_1}{\gamma}\)

(C) \(a_1\alpha + b_1\beta + c_1\gamma = 0\)

(D) None of these

Answer 1

Correct answer is (B) \(\frac{a_1}{\alpha} = \frac{b_1}{\beta} = \frac{c_1}{\gamma}\)