Vectors Parallel Perpendicular Plane

Let P be a plane passing through the points (1,0,1),(1,−2,1) and (0,1,−2). Let a vector

→

a

=α

^

i

+β

^

j

+γ

^

k

be such that

→

a

is parallel to theplane P, perpendicular to (

^

i

+2

^

j

+3

^

k

) and

→

a

.(

^

i

+

^

j

+2

^

k

)=2, then (α−β+γ)2 equals _______.