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MHT CET202525 Apr 2025Morning ShiftMathematicsThree Dimensional GeometryActual

If the lines 1-x 2 = 7 y+4 2 = 2 z-5 2 and 7-7 x 3 = y-1 7 = 6-z 5 are at right angle, then the value of is

Options

  1. A4 7
  2. B7 4
  3. C20 7
  4. D5 4

Correct answer

B. 7 4

Step-by-step solution

The condition for perpendicular lines requires that the dot product of their direction vectors is zero. For lines in the form x-x₁ a = y-y₁ b = z-z₁ c , the direction ratios are (a, b, c) . Rewriting the first equation 1-x 2 = 7y+4 2 = 2z-5 2 in standard form gives direction ratios (-2, 2 7 , 1) . The second equation 7-7x 3 = y-1 7 = 6-z 5 yields direction ratios (- 3 7 , 7, -5) . Setting the dot product to zero: (-2)(- 3 7 ) + ( 2 7 )(7) + (1)(-5) = 0 Simplifying: 6 7 + 2 - 5 = 0 Multiplying through by 7: 6 + 14 -

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