If `|a|=|b|=1 and |a+b|=sqrt(3)`, then the value of `(3a-4b)(2b+5b)` is

Options

A. `-21`
B. `-(21)/(2)`
C. `21`
D. `(21)/(2)`

Answer

B

Explanation

Given ,`|a|=|b|=1 and |a+b|=sqrt(3)`
`rArr |a|^2+|b|^2+2a.b=3`
`a.b=(1)/(2)[because|a|^2=1|b|^2=1]`
`therefore(3a-4b).(2a+5b)=6|a|^2+15a.b-8a.b-20|b|^2`
`=6+7a.b-20=-(21)/(2)[becausea.b=(1)/(2)]`