Question

Let the vectors `veca and vecb` be such that `|veca|=3and|vecb|=sqrt2/3"then|" vecaxxvecb`is a unit vector. If the angle between `veca and vecb` is ?

Answer 1

It is given that `|veca|=3and |vecb|=sqrt2/3`
we know that `vecaxxvecb= |veca|vecb|sin theta hatn "where" hatn` is a unit vector peroendicular to both `veca and vecb and theta` is the angle between `veca and vecb`.
`now veca xx vecb` is a unit vector if `|vecaxxvecb|=1`
` or , ||veca||vecb|sin theta|=1`.
`or , ||veca||vecb| sin theta|=1`
`or 3xxsqrt2/3xxsintheta=1`
`or theta=pi/4`
Hence , `veca xx vecb` is a unit vector if the angle between `veca and vecb is pi/4`.