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MHT CET20244 May 2024Morning ShiftMathematicsThree Dimensional GeometryActual

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

Options

  1. A- i +7 j +7 k 99
  2. B- i -7 j +5 k 5 3
  3. C- i +7 j +5 k 5 3
  4. D7 i -7 j -7 k 99

Correct answer

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

Step-by-step solution

Vector perpendicular to L ₁ and L ₂ is L ₁ L ₂ aligned & L ₁ L ₂= | array ccc i & j & k 3 & 1 & 2 1 & 2 & 3 array |=- i -7 j +5 k & Required unit vector = - i -7 j +5 k (-1)^2+(-7)^2+(5)^2 & = - i -7 j +5 k 75 = - i -7 j +5 k 5 3 aligned

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