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KCET2024MathematicsThree Dimensional Geometry

If lines x-1 -3 = y-2 2 k = z-3 2 and x-1 3 k = y-5 1 = z-6 -5 are mutually perpendicular, then k is equal to

Options

  1. A- 10 7
  2. B- 7 10
  3. C-10
  4. D-7

Correct answer

A. - 10 7

Step-by-step solution

x-1 -3 = y-2 2 k = z-3 2 and x-1 3 k = y-5 1 = z-6 -5 b ₁=-3 i +2 j +2 k and b ₂=3 k i + j -5 k Now, b ₁ b ₂= 0 -9 k+2 k-10=0 -7 k=10 k= -10 7 Hence, the value of k is - 10 7

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