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Let vec a and vec b be unit vectors suc...

Let ` vec a and vec b` be unit vectors such that `| vec a+ vec b|=sqrt(3)` . Then find the value of `(2 vec a+5 vec b).((3 vec a+ vec b+ vec axx vec b))dot`

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`(2veca+5vecb).(3veca+vecb+vecaxxvecb)=6veca.veca+17veca.vecb+5vecb.vecb=11+17veca.vecb`
`(veca.(vecaxxvecb)=vecb.(vecaxxvecb)=0,as veca and vecb` are perpendicular to `veca xx vecb`)
`|veca+vecb|=sqrt3`
`|veca+vecb|^(2)=3`
`|veca|^(2)+|vecb|^(2)+2veca.vecb=3`
`veca.vecb=1/2`
`Rightarrow (2veca+5vecb).(3veca+vecb+veca xx vecb)11+17/2=39/2`
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