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MHT CET20192 May 2019Morning ShiftMathematicsThree Dimensional GeometryActual

The equation of the plane passing through the point - 1 , 2 , 1 and perpendicular to the line joining the points - 3 , 1 , 2 and 2 , 3 , 4 is ________

Options

  1. Ar - . 5 i ^ + 2 j ^ + 2 k ^ = 1
  2. Br - . 5 i ^ + 2 j ^ + 2 k ^ = - 1
  3. Cr - . 5 i ^ - 2 j ^ + 2 k ^ = - 5
  4. Dr - . 5 i ^ - 2 j ^ - 2 k ^ = 1

Correct answer

A. r - . 5 i ^ + 2 j ^ + 2 k ^ = 1

Step-by-step solution

Since, direction ratio of normal Are 2 - - 3 , 3 - 1 , 4 - 2 = 5 , 2 , 2 Then, equation of plane is 5 x + 1 + 2 y - 2 + 2 z - 1 = 0 = 5 x + 2 y + 2 z - 1 = 0 = r . ¯ 5 i + 2 j + 2 k = 1 Or Equation of plane passing through a ¯ = - i + 2 j - k and the position vector of normal n ¯ = 5 i + 2 j + 2 k is r ¯ - a ¯ . n ¯ = 0 , r . ¯ 5 i + 2 j + 2 k = 1

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