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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 |
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Answer» Solution :`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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