Let the foot of perpendicular from the point {\A}(4,3,1) on the plane {\P}: {\x}- {\y}+2 {\z}+3=0 be {\N}. If {\B}(5, \alpha, \beta), \alpha, \beta \in {\Z} is a point on plane P such that the area of the triangle A B N is 3 \sqrt{2}, then \alpha^2+\beta^2+\alpha \beta is equal to _______. [10-Apr-2023 shift 2]

JEE Mains 10-Apr-2023 Shift 2 Solved Paper

Section: Mathematics

Question : 26 of 90

Marks: +1, -0

Let the foot of perpendicular from the point A(4,3,1) on the plane P:x−y+2z+3=0 be N. If B(5,α,β), α,β∈Z is a point on plane P such that the area of the triangle ABN is 3√2, then α2+β2+αβ is equal to _______.

[10-Apr-2023 shift 2]

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