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BITSAT2023MathematicsThree Dimensional GeometryActual

The shortest distance between the lines x = y +2=6 z-6 and x+1=2 y=-12 z is

Options

  1. A1 2
  2. B2
  3. C1
  4. D3 2

Correct answer

B. 2

Step-by-step solution

The lines are x 6 = y+2 6 = z-1 1 and x+1 12 = y 6 = z -1 Here, aligned & a ₁=-2 j + k , b₁+6 i +6 j + k , a ₂=- i , & b ₂=12 i +6 j - k & b ₁ b ₂= | array ccc i & j & k 6 & 6 & 1 12 & 6 & -1 array |=-12 i +18 j -36 k & Shortest distance = | ( a ₂- a ₁ ) ( b ₁- b ₂ ) | | b ₁ b ₂ | aligned aligned & = |(- i +2 j - k ) (-12 i+18 j -36 k )| (-12)^2+(18)^2+(-36)^2 & = |+12+36+36| 1764 = 84 42 =2 aligned

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