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JEE Main20202 Sep 2020Evening ShiftMathematicsThree Dimensional GeometryActual

A plane passing through the point 3 , 1 , 1 contains two lines whose direction ratios are 1 , – 2 , 2 and 2 , 3 , – 1 respectively. If, this plane also passes through the point α , – 3 , 5 , then α is equal to

Options

  1. A5
  2. B- 10
  3. C10
  4. D- 5

Correct answer

A. 5

Step-by-step solution

Plane is a ( x - 3 ) + b ( y - 1 ) + c ( z - 1 ) = 0 Direction ratios of lines are 1 ,   - 2 ,   2 ,   2 ,   3 ,   - 1 . Since both lines lie in to the plane implies dot product of direction ratios of line with direction ratio of normal of plane will be zero. ⇒ a - 2 b + 2 c = 0 ⇒ 2 a + 3 b - c = 0 a - 4 = b - - 5 = c 7 ⇒ a 4 = b - 5 = c - 7 ∴ Direction ratios of normal of plane 4 , - 5 , - 7 ∴ Equation of plane is 4 x - 5 y - 7 z = 0 α , - 3 , 5 lies on p

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