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If vec(a)_(1) and vec(a)_(2) are two non collinear unit vectors and if |vec(a)_(1) + vec(a)_(2)|= sqrt3, 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 = (sqrt3)^(2)= 3 or 1 + 1 + 2 cos 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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