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

Options

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

Answer

B

Explanation

`because|a+b|=sqrt3rArr|a|^2+|b|^2+2a*b=3`
`rArr" "a*b=(3-1-1)/2=1/2" ...(i) "[because|a|=|b|=1, "given"]`
`:." "(3a-4b)*(2a+5b)=6|a|^2+15a*b-20|b|^2`
`=6+7a*b-20`
`=6+7/2-20" [from Eq. (i)]"`
`=(7-28)/2-21/2`