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MHT CET202617 April 2026Morning ShiftMathematicsThree Dimensional GeometryActual

If the lines r = i + j - k + (q i - 2 j + k ) and r = p i - 3 j + 2 k + ( i - 2 j + 2 k ) intersect each other and q i - 2 j + k is collinear to 4 i - 4 j + 2 k , then the values of p and q are

Options

  1. Ap = 4, q = 3
  2. Bp = 2, q = 3
  3. Cp = 4, q = 2
  4. Dp = 4, q = 1

Correct answer

C. p = 4, q = 2

Step-by-step solution

Given that the vector q i - 2 j + k is collinear to 4 i - 4 j + 2 k , their direction ratios must be proportional. q 4 = -2 -4 = 1 2 q = 2 The equations of the lines become: r = i + j - k + (2 i - 2 j + k ) r = p i - 3 j + 2 k + ( i - 2 j + 2 k ) Since the lines intersect, their general points must coincide for some values of and . Equating the respective components, we get: 1 + 2 = p + 1 - 2 = -3 - 2 -1 + = 2 + 2 From the second equation: 2 - 2 = 4 - = 2 From the third equation: - 2 = 3 Subtracting the third equat

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