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MHT CET20243 May 2024Evening ShiftMathematicsVector AlgebraActual

Let L ₁ x+1 3 = y+2 2 = z+1 1 and L₂: x-2 2 = y+2 1 = z-3 3 be the given lines. Then the unit vector perpendicular to L₁ and L₂ is

Options

  1. A-5 i +7 j +2 k 78
  2. B5 i -7 j + k 5 3
  3. C5 i -7 j - k 5 3
  4. D5 i +7 j - k 5 3

Correct answer

C. 5 i -7 j - k 5 3

Step-by-step solution

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

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