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Question

Mathematics Question on Three Dimensional Geometry

Let αx+βy+yz=1\alpha x+\beta y+y z=1 be the equation of a plane passing through the point (3,2,5)(3,-2,5) and perpendicular to the line joining the points (1,2,3)(1,2,3) and (2,3,5)(-2,3,5) Then the value of αβy\alpha \beta y is equal to ____

Answer

The correct answer is 6.
Given Equation is not equation of plane as yy is present. If we consider y is γ then answer would be 6 .
Normal vector of plane =3i^−j^​−2k^
Plane :3x−y−2z+λ=0
Point (3,−2,5) satisfies the plane
λ=−1
3x−y−2z=1
αβy=6