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MHT CET202415 May 2024Morning ShiftMathematicsThree Dimensional GeometryActual

Let L ₁: x+2 5 = y-3 2 = z-6 1 and L ₂: x-3 4 = y+2 3 = z-3 5 be the given lines, Then the unit vector perpendicular to both L ₁ and L ₂ is

Options

  1. A- i -3 j + k 11
  2. Bi -3 j + k 11
  3. Ci +3 j - k 11
  4. Di +3 j + k 11

Correct answer

B. i -3 j + k 11

Step-by-step solution

Lines L₁ and L₂ are parallel to the vectors b ₁=5 i +2 j + k and b ₂=4 i +3 j +5 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 5 & 2 & 1 4 & 3 & 5 array |=7 i -21 j +7 k aligned n & = 7 i -21 j +7 k 539 & = 7( i -3 j + k ) 7 11 = i -3 j + k 11 aligned [Note: The answer of the question is not mentioned as an option.]

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