IIM B UG (B.Sc-Hons.)- Sample Paper 2026 · Quant & DI · Question 20
IIM B UG (B.Sc-Hons.)- Sample Paper 2026 question on Three Dimensional Geometry, with the answer and a step-by-step solution.
What is the shortest distance between the lines below, where s, t are real numbers?
- A
3 unit
- B
\sqrt{3} units
- C
\sqrt{2} units
- D
1 unit
Answer & solution
Answer: Option B
The first line passes through a₁ = (1, 0, 0) with direction d₁ = (1, 1, 0).
The second passes through a₂ = (0, 1, 1) with direction d₂ = (1, 0, 1).
The directions are not parallel, so the lines are skew and the shortest distance is |(a₂ − a₁) · (d₁ × d₂)| ÷ |d₁ × d₂|.
d₁ × d₂ = (1·1 − 0·0, 0·1 − 1·1, 1·0 − 1·1) = (1, −1, −1).
Its magnitude is √(1 + 1 + 1) = √3.
a₂ − a₁ = (−1, 1, 1).
The dot product is (−1)(1) + (1)(−1) + (1)(−1) = −3.
Shortest distance = |−3| ÷ √3 = 3/√3 = √3 units.
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