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MHT CET20242 May 2024Evening ShiftMathematicsThree Dimensional GeometryActual

Distance between the parallel lines x 3 = y-1 -2 = z 1 and x+4 3 = y-3 -2 = z+2 1 is

Options

  1. A6 7 units
  2. B3 7 units
  3. C3 14 units
  4. D5 14 units

Correct answer

A. 6 7 units

Step-by-step solution

The vector equations of the given lines are aligned & r = j + (3 i -2 j + k ) and & r =-4 i +3 j -2 k + (3 i -2 j + k ) aligned The distance between the parallel lines r = a ₁+ b and r = a ₂+ b is given by d= | ( a ₂- a ₁ ) b | b | | aligned & Here, a ₁= j , a ₂=-4 i +3 j -2 k , b =3 i -2 j + k & a ₂- a ₁=-4 i +2 j -2 k aligned aligned & ( a ₂- a ₁ ) b = | array ccc i & j & k -4 & 2 & -2 3 & -2 & 1 array | & =-2 i -2 j +2 k & | b |= 9+4+1 = 14 aligned aligned d & = | -2 i -2 j +2 k 14 | & = 4+4+4 14 & = 12 14 = 6 7

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