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JEE Main202117 Mar 2021Evening ShiftMathematicsThree Dimensional GeometryActual

Let P be an arbitrary point having sum of the squares of the distance from the planes x + y + z = 0 , l x - n z = 0 and x - 2 y + z = 0 equal to 9 units. If the locus of the point P is x 2 + y 2 + z 2 = 9 , then the value of l - n is equal to

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The distance of a point x 1 ,   y 1 ,   z 1 from a plane a x + b y + c z + d = 0 is a x 1 + b y 1 + c z 1 + d a 2 + b 2 + c 2 . Given the point P is an arbitrary point such that the sum of the squares of its distance from the planes x + y + z = 0 ,   l x - n z = 0 and x - 2 y + z = 0 is equal to 9 units. Let, the point P is α ,   β ,   γ , then we have α + β + γ 3 2 + l α - n γ l 2 + n 2 2 + α - 2 β + γ 6 2 = 9 Thus, the locus can be ob

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