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JEE Main20199 Apr 2019Morning ShiftMathematicsThree Dimensional GeometryActual

A plane passing though the points ( 0 , - 1, 0 ) and ( 0 , 0, 1 ) and making an angle π 4 with the plane y – z + 5 = 0 , also passes through the point

Options

  1. A( 2 ,   - 1,   4 )
  2. B( 2 ,   1,   4 )
  3. C( - 2 ,   - 1 ,   - 4 )
  4. D( - 2 ,   1 ,   - 4 )

Correct answer

B. ( 2 ,   1,   4 )

Step-by-step solution

The equation of a plane passing through a point x 1 ,   y 1 ,   z 1 and having direction ratios of the normal to the plane as < a ,   b ,   c > is a x - x 1 + b y - y 1 + c z - z 1 = 0 . Thus, the equation of the plane passing through 0 ,   - 1 ,   0 is a x - 0 + b y + 1 + c z - 0 = 0 ⇒ a x + b y + c z + b = 0 ∵ It passes through 0 ,   0 ,   1 ⇒ c = - b ∴ Equation of plane is a x + b y - b z + b = 0       … i ∵ It mak

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