If `veca and vecb` are vectors in space given by `veca= (hati-2hatj)/sqrt5and vecb= (2hati + hatj + 3hatk)/sqrt14` then find the value of `(2veca + vecb) . [(vecaxxvecb) xx (veca- 2vecb)]`

Answer

5

Explanation

`E= (2veca + vecb).[|veca|^(2) vecb-(veca.vecb)veca-2(veca.vecb)vecb +2|vecb|^(2)veca]`
`veca.vecb= (2-2)/sqrt70=0`
`|veca|=1`
`|b|=1`
`E= (2veca+vecb).[ 2|vecb|^(2)veca + |veca|^(2)vecb]`
`4|veca|^(2)|vecb|^(2)+|veca|^(2)(veca.vecb)`
`+2|vecb|^(2)(vecb.veca)+|veca|^(2)|vecb|^(2)`
`5|veca|^(2)|vecb|=5`