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JEE Main202131 Aug 2021Morning ShiftMathematicsThree Dimensional GeometryActual

The square of the distance of the point of intersection of the line x - 1 2 = y - 2 3 = z + 1 6 and the plane 2 x - y + z = 6 from the point ( - 1 , - 1 , 2 ) is

Correct answer

61

Step-by-step solution

Equation of line x - 1 2 = y - 2 3 = z + 1 6 Let x - 1 2 = y - 2 3 = z + 1 6 = λ ⇒ x   =   2 λ + 1 ,   y   =   3 λ + 2 ,   z = 6 λ - 1 ⇒    Let P ( 2 λ + 1 , 3 λ + 2 , 6 λ - 1 ) is point of intersection of line and plane So it should satisfy the given plane. ⇒    2 ( 2 λ + 1 ) - 3 λ - 2 + 6 λ - 1 = 6 7 λ = 7 ⇒ λ = 1 Point P ( 3 , 5 , 5 ) Square of distance from point ( - 1 , - 1 , 2

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