Let the system of linear equations -x+2 y-9 z=7 -x+3 y+7 z=9 -2 x+y+5 z=8 -3 x+y+13 z=λ has a unique solution x=α, y=β, z=γ. Then the distance of the point (α, β, γ) from the plane 2 x-2 y+z=λ is:

Three Dimensional Geometry: JEE Main 2023 Mathematics question

JEE Main 2023 · 15 Apr, Morning shift · Q2606

JEE Main 202315 Apr, Morning shiftMathematicsMediumThree Dimensional Geometry249× since 2002

Let the system of linear equations

-x+2 y-9 z=7

-x+3 y+7 z=9

-2 x+y+5 z=8

-3 x+y+13 z=\lambda

has a unique solution

x=\alpha, y=\beta, z=\gamma

. Then the distance of the point

(\alpha, \beta, \gamma)

from the plane

2 x-2 y+z=\lambda

is :