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JEE Main20238 Apr 2023Morning ShiftMathematicsThree Dimensional GeometryActual

If the equation of the plane containing the line x + 2 y + 3 z - 4 = 0 = 2 x + y - z + 5 and perpendicular to the plane r → = i ^ - j ^ + λ i ^ + j ^ + k ^ + μ ( i ^ - 2 j ^ + 3 k ^ ) is a x + b y + c z = 4 then ( a - b + c ) is equal to

Options

  1. A18
  2. B22
  3. C20
  4. D24

Correct answer

B. 22

Step-by-step solution

Given, The equation of the plane containing the line x + 2 y + 3 z - 4 = 0 = 2 x + y - z + 5 and perpendicular to the plane r → = i ^ - j ^ + λ i ^ + j ^ + k ^ + μ ( i ^ - 2 j ^ + 3 k ^ ) is a x + b y + c z = 4 , Now let equation of required plane be, P :   x + 2 y + 3 z - 4 + α 2 x + y - z + 5 = 0 ⇒ ( 2 α + 1 ) + α + 2 y + 3 - α z = 4 - 5 α So, the normal vector is given by, n 1 → = ( 2 α + 1 ) i ^ + ( α + 2 ) j ^ + ( 3 - α ) k ^ And normal o

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