If `veca` and `vecb` are two non-collinear unit vectors and if `|veca_(1) + veca_(2)|=sqrt(3)`, then the value of `(veca_(1) -veca_(2))(2veca_(1) +veca_(2))` is:

Options

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

Answer

B

Explanation

`|veca_(1) + veca_(2)|= 3`
`sqrt((1)^(2) + (1)^(2)+ 2(1)(1) cos theta )= sqrt(3)`
`" "= 2 + 2 cos theta = 3`
`therefore " "cos theta = 1//2`
Now,
`(veca_(1) - veca_(2)). (2veca_(1) + veca_(2)) = 2veca_(1). veca_(1) - veca_(2).veca_(2)- 2veca_(1). veca_(2) + veca_(1).veca_(2)`
`= 2(1) -(1) - 2cos theta + cos theta`
`= 1 - cos theta = 1- (1)/(2)= (1)/(2)`