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Question:

Three lines L_1 = r⃗ = λi, λ ∈ R, L_2 = r⃗ = k + μj, μ ∈ R, and L_3 = r⃗ = i + vj + vk, v ∈ R are given. For which point(s) Q on L_2 can we find a point P on L_1 and a point R on L_3 so that P, Q, and R are collinear?

k−1;2j^

k+12j^

k+j^

k^

Solution:

Correct option is D. k−1;2j^
P(λ,0,0) Q(0,μ,1) R(1,1,γ)
PQ→ = k
PR→ = λ
λ−1; = −μ−1; = −1;
−γ
⇒ 1+λ−1; μ = −1; −γ
μ cannot take value of 1 and 0