Vector!!

A silly question indeed...
just started reading vectors and i got confused..

Got the full solution but am not satisfied... :(

suppose

(a-b)=cx(λ₁a+λ₂b)...................................(i)

then what should be conditions on them...

i easily got the answer multiplied .c on both sides so easily got the answer

a.c=b.c

But my doubt is......

i am not able to see what is the conclusion of the answer..

(a-b) lies in same plane as of (λ₁a+λ₂b) so how cross product of (λ₁a+λ₂b) with a vector c gives a vector in the same plane of (λ₁a+λ₂b)