1.

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

Answer»

`-21`
`-21/2`
`21`
`21/2`

Solution :`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`


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