If `vec(a)_(1)` and `vec(a)_(2)` are two collinear unit vectors and if `|vec(a)_(1)+vec(a)_(2)|=sqrt(3)`, then the value of `(vec(a)_(1)-vec(a)_(2)).(2vec(a)_(1)+vec(a)_(2))` is

Explanation

`a_(1)=a_(2)=1` and `a_(1)^(2)+a_(2)^(2)+2a_(1)a_(2)cos theta = (sqrt(3))^(2)=3` or `1+1+2cos theta=3` or `cos theta = 1//2`
Now `(vec(a)_(1)vec(a)_(2)).(2vec(a)_(1)+vec(a)_(2))=2a_(1)^(2)-a_(2)^(2)-a_(1)a_(2)cos theta`
`= 2-1-(1)/(2)=(1)/(2)`