Given `|veca|=|vecb|=1 and |veca + vecb|= sqrt3` if `vecc` is a vector such that `vecc -veca - 2vecb = 3(veca xx vecb) ` then find the value of `vecc . vecb`.

Explanation

We, have, `|veca + vecb|=sqrt3`
` or |veca + vecb|^(2) =3`
`or |veca|^(2) + |vecb|^(2) + 2(veca .vecb) =3`
`or veca. Vecb = 1//2` (i)
now ` vecc - veca - 2vecb = 3(veca xx vecb) `
`or (vecc - veca - 2vecb) .vecb = 3{(veca xx vecb) .vecb}`
`or vecc . vecb - 1/2 - 2xx 1 =0`
or `vecc.vecb = 5//2`