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MHT CET202619 April 2026Evening ShiftMathematicsThree Dimensional GeometryActual

Let r (3 i - 2 j + 7 k ) = 32 is the equation of a plane and the line having direction ratios (5, b, 3) is parallel to the plane, then the value of b is...

Options

  1. Ab = 13
  2. Bb = 15
  3. Cb = 16
  4. Db = 18

Correct answer

D. b = 18

Step-by-step solution

The equation of the plane is r (3 i - 2 j + 7 k ) = 32 . The normal vector to the plane is n = 3 i - 2 j + 7 k . The direction vector of the line is d = 5 i + b j + 3 k . Since the line is parallel to the plane, its direction vector is perpendicular to the normal vector of the plane. n d = 0 (3)(5) + (-2)(b) + (7)(3) = 0 15 - 2b + 21 = 0 36 - 2b = 0 b = 18 Answer: b = 18

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