Given two vectors [latex]\mathbf{a}=2\mathbf{i}+\mathbf{j}-2\mathbf{k}[/latex] and [latex]\mathbf{b}=\mathbf{j}+3\mathbf{k}[/latex], find:
(i)
a unit vector perpendicular to both [latex]\mathbf{a}[/latex] and [latex]\mathbf{b}[/latex].
(ii)
the exact value of [latex]\sin \theta [/latex], where [latex]\theta [/latex] is the angle between [latex]\mathbf{a}[/latex] and [latex]\mathbf{b}[/latex].