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The shortest distance between r = (1,2,3) + λ(2,3,4) and r = (2,4,5) + μ(3,4,5) is
A1/√6
B2/√6
C1/3
D0
Answer & Solution
Correct answer: A. 1/√6
1. Connecting vector a₂ - a₁ = (1, 2, 2).
2. b₁ × b₂ = (3·5 - 4·4, 4·3 - 2·5, 2·4 - 3·3) = (-1, 2, -1).
3. |b₁ × b₂| = √(1+4+1) = √6.
4. Scalar triple product: 1(-1) + 2(2) + 2(-1) = -1+4-2 = 1. Distance = |1|/√6 = 1/√6.
_Source: NCERT Class 12 Maths Part 2 Ch 11 "Three Dimensional Geometry", §11.5.1_
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