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If a(1) and a(2) aare two non- collineaa...

If `a_(1) and a_(2)` aare two non- collineaar unit vectors and if `|a_(1)+a_(2)|=sqrt(3),` ,then value of `(a_(1)-a_(2)).(2a_(1)-a_(2))` is

A

2

B

`(3)/(2)`

C

`(1)/(2)`

D

1

Text Solution

Verified by Experts

The correct Answer is:
B
(b) Since `a_(1)and a_(2)` are non -colllinear
`therefore a_(1)=a_(2)=1`
`and |a_(1)+a_(2)|=sqrt(3)`
`implies a_(1)^(2)+a_(2)^(2)+2a_(1)a_(2)cos theta=(sqrt(3))^(2)`
` implies 1+1+2cos theta=3=. costheta=(1)/(2)`
`Now ,(a_(1)-a_(2).(2a_(1)-a_(2))=2a_(1)^(2)-a_(1).a_(2)-2a_(1).a_(2)+A_(2)^(2)`
`=2s_(1)^(2)+a_(2)^(2)-3a_(1)a_(2)costheta`
`=2+1-(3)/(2)=3//2`
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