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← JEE Main 2026 · 4 Apr · Shift 2
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JEE Main 2026 · 4 Apr · Shift 2, Mathematics question 13

The shortest distance between the lines r⃗=(13i^+2j^+83k^)+λ(2i^−5j^+6k^)\vec r=\left(\dfrac13\hat i+2\hat j+\dfrac83\hat k\right)+\lambda\left(2\hat i-5\hat j+6\hat k\right) and r⃗=(−23i^−13k^)+μ(j^−k^)\vec r=\left(-\dfrac23\hat i-\dfrac13\hat k\right)+\mu\left(\hat j-\hat k\right), λ,μ∈R\lambda,\mu\in\mathbb R, is:

Choose one option
Answer and worked solution

Official answer: B

Common normal. (2,−5,6)×(0,1,−1)=(−1,2,2)(2,-5,6)\times(0,1,-1)=(-1,2,2), of length 3.

Join the points. a⃗2−a⃗1=(−1,−2,−3)\vec a_2-\vec a_1=(-1,-2,-3), and its dot product with the normal is 1−4−6=−91-4-6=-9.

Distance 93=3\frac93=3.

(B)

Topics:Skew lines
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