\(\, = \,\,\left( {\frac{{\,\mathop A\limits^ \to .\,\mathop B\limits^ \to \,}}{B}} \right)\,\hat B\,\, = \,\,\left( {\frac{{\,\mathop A\limits^ \to .\,\mathop B\limits^ \to }}{B}} \right)\,\frac{{\mathop B\limits^ \to }}{B}\,\)
\(\, = \,\,\left[ {\frac{{\left( {3\hat i\,\, + \;\,\hat j} \right)\,\,\left( {\hat j\,\, + \;\,2\hat k} \right)}}{{\sqrt 5 }}} \right]\,\,\frac{{\left( {\hat j\,\, + \;\,2\hat k} \right)}}{{\sqrt 5 }}\)
\( = \,\,\frac{1}{5}\,\,\left( {\hat j\,\, + \;\,2\hat k} \right)\)