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Three Dimensional Geometry · Class 12 · CBSE · Science Mathematics

The shortest distance between the skew lines r = (1, 0, 1) + λ(1, 1, 0) and r = (0, 1, 0) + μ(1, 0, 1) is:

Practice question from Three Dimensional Geometry (Class 12 · CBSE · Science Mathematics), with the correct answer and a step-by-step solution.

hard · MCQ · Q-5BB42A

The shortest distance between the skew lines r = (1, 0, 1) + λ(1, 1, 0) and r = (0, 1, 0) + μ(1, 0, 1) is:

  1. A.1/√3Correct answer
  2. B.√3
  3. C.1
  4. D.2/√3

Solution

For the direction vectors a=(1,1,0)\mathbf a=(1,1,0) and b=(1,0,1)\mathbf b=(1,0,1), a×b=(1,−1,−1)\mathbf a\times\mathbf b=(1,-1,-1). Using d=∣(b0−a0)⋅(a×b)∣∣a×b∣d=\frac{|(\mathbf b_0-\mathbf a_0)\cdot(\mathbf a\times\mathbf b)|}{|\mathbf a\times\mathbf b|} gives d=13d=\frac{1}{\sqrt3}.

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