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JEE Main20238 Apr 2023Morning ShiftMathematicsThree Dimensional GeometryActual

Let λ 1 ,   λ 2 be the values of λ for which the points 5 2 , 1 ,   λ and - 2 ,   0 ,   1 are at equal distance from the plane 2 x + 3 y - 6 z + 7 If λ 1 > λ 2 then the distance of the point λ 1 - λ 2 , λ 2 , λ 1 from the line x - 5 1 = y - 1 2 = z + 7 2 is _ _ _ _ _ _

Correct answer

9

Step-by-step solution

Given, λ 1 ,   λ 2 be the values of λ for which the points 5 2 , 1 ,   λ and - 2 ,   0 ,   1 are at equal distance from the plane 2 x + 3 y - 6 z + 7 , So, by using distance formula of a point from a plane we get, - 4 + 0 - 6 + 7 2 2 + 3 2 + 6 2 = 5 + 3 - 6 λ + 7 2 2 + 3 2 + 6 2 ⇒ - 4 + 0 - 6 + 7 7 = 5 + 3 - 6 λ + 7 7 ⇒ 3 7 = 15 - 6 λ 7 ⇒ λ = 2 or 3 ⇒ λ 1 = 3 ,   λ 2 = 2 as λ 1 >   λ 2 So, λ 1

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