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BITSAT2023MathematicsThree Dimensional GeometryActual

The shortest distance between the lines x-3 2 = y-2 3 = z-1 -1 and x+3 2 = y-6 1 = z-5 3 is :

Options

  1. A18 5
  2. B22 3 5
  3. C46 3 5
  4. D6 3

Correct answer

A. 18 5

Step-by-step solution

Give lines are x-3 2 = y-2 3 = z-1 -1 and x+3 2 = y-6 1 = z-5 3 Lines passes through the points a ₁=(3,2,1) and a ₂=(-3,6,5) , b ₁=2 i +3 j - k b ₁=2 i + j -3 k , a ₂- a ₁=6 i -4 j-4 k Shortest distance = | ( a ₂- a ₁ ) ( b ₁ b ₂ ) | | ( b ₁ b ₂ ) | b ₁ b ₂= | array ccc i & j & k 2 & 3 & -1 2 & 1 & 3 array |=10 i -8 j -4 k ( a ₂- a ₁ ) ( b ₁ b ₂ )=60+32+16=108 | b ₁ b ₂ |= 100+64+16 = 180 S . D= 108 180 = 108 6 5 = 18 5

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