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

Options

A. 2
B. `(3)/(2)`
C. `(1)/(2)`
D. 1

Answer

B

Explanation

(b) Since, `a_(1)anda_(2)` are non-collinear
`:.a_(1)=a_(2)=1`
` "and "|a_(1)+a_(2)|=sqrt(3)`
`rArra_(1)^(2)+a_(2)^(2)+2a_(1)a_(2)costheta=(sqrt(3))^(2)`
`rArr1+1+2costheta=3`
`rArrcostheta=(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)`
`=2a_(1)^(2)+a_(2)^(2)-3a_(1)a_(2)costheta`
`=2+1-(3)/(2)=3//2`