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If a(1) and a(2) are two non-collinear u...

If `a_(1)` and `a_(2)` are two non-collinear unit vector with `|a_(1)+a_(2)|=sqrt(3)`, then the value of `(a_(1)-a_(2))(2a_(1)+a_(2))` is

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`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)`
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