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Paragraph: Consider the lines: L₁: x+1 3 = y+2 1 = z+1 2 , L₂: x-2 1 = y+2 2 = z-3 3 Question: The unit vector perpendicular to both 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 - k 99

Correct answer

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

Step-by-step solution

The equations of given lines in vector form may be written as L₁: r (- i -2 j - k )+ (3 i + j +2 k ) and L₂: r =(2 i -2 j +3 k )+ ( i +2 j +3 k ) The vector perpendicular to both L₁ and L₂ is | array rrr i & j & k 3 & 1 & 2 1 & 2 & 3 array |=- i -7 j +5 k aligned Required unit vector & = (- i -7 j +5 k ) (-1)^2+(-7)^2+(5)^2 & = 1 5 3 (- i -7 j +5 k ) aligned

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