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MHT CET202615 April 2026Morning ShiftMathematicsThree Dimensional GeometryActual

The direction cosines of a line which is perpendicular to the lines x-7 2 = y+17 -3 = z-6 1 and x+5 1 = y+3 2 = z-6 -2 are...

Options

  1. A4 3 10 , 5 3 10 , 7 3 10
  2. B4 3 10 , 5 3 10 , 7 3 10
  3. C4 3 10 , 5 3 10 , 7 3 10
  4. D4 3 10 , 5 3 10 , 7 3 10

Correct answer

D. 4 3 10 , 5 3 10 , 7 3 10

Step-by-step solution

Let the direction ratios of the required line be a, b, c . Since the line is perpendicular to the given lines, its direction ratios satisfy: 2a - 3b + c = 0 a + 2b - 2c = 0 Solving by cross-multiplication: a (-3)(-2) - (1)(2) = b (1)(1) - (2)(-2) = c (2)(2) - (-3)(1) a 6 - 2 = b 1 + 4 = c 4 + 3 a 4 = b 5 = c 7 The direction ratios are proportional to 4, 5, 7 . The magnitude is 4^2 + 5^2 + 7^2 = 16 + 25 + 49 = 90 = 3 10 . Therefore, the direction cosines are 4 3 10 , 5 3 10 , 7 3 10 .

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