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MHT CET202314 May 2023Morning ShiftMathematicsThree Dimensional GeometryActual

Consider the lines aligned & L ₁: x+1 3 = y+2 1 = z +1 2 & ~L ₂: x-2 1 = y+2 2 = z-3 3 aligned then the unit vector perpendicular to both L ₁ and L ₂ is

Options

  1. A- i +7 j +5 k 5 3
  2. B- i -7 j +5 k 5 3
  3. C+ i -7 j +5 k 5 3
  4. Di +7 j +5 k 5 3

Correct answer

B. - i -7 j +5 k 5 3

Step-by-step solution

Lines L₁ and L₂ are parallel to the vectors b ₁=3 i + j +2 k and b ₂= i +2 j +3 k respectively. The unit vector perpendicular to both L ₁ and L ₂ is n = b ₁ b ₂ | b ₁ b ₂ | Now, b ₁ b ₂= | array lll i & j & k 3 & 1 & 2 1 & 2 & 3 array |=- i -7 j +5 k n = 1 5 3 (- i -7 j +5 k )

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