The unit vector parallel to the resultant of the vectors   $\overrightarrow{A}=4\widehat{i}+3\widehat{j}+6\widehat{k}$ and  $B=-\widehat{i}+3\widehat{j}-8\widehat{k}$  is 

 $$\begin{gathered} A=4\widehat{i}+3\widehat{j}+6\widehat{k} \\ B=-\widehat{i}+3\widehat{j}-8\widehat{k} \end{gathered}$$
 unit vector  parallel  to resultant vector is 
 $$\begin{gathered} R=A+B \\ =4i+3j+6k-i+3j-8k \\ =3i+6j-2k \\ \widehat{R}=\frac{\overline{R}}{\left|\overline{R}\right|}=\frac{3i+6j-2k}{\sqrt{9+36+4}} \\ =\frac{3i+6j-2k}{7} \end{gathered}$$