A unit vector pependicular to the plane of 
$\overline{\mathrm{a}}=2\overline{\mathrm{i}}-6\overline{\mathrm{j}}-3\overline{\mathrm{k}}, \overline{\mathrm{b}}=4\overline{\mathrm{i}}+3\overline{\mathrm{j}}-\overline{\mathrm{k}}$ is

$$\begin{gathered} \overline{\mathrm{a}}\times \overline{\mathrm{b}}=\left|\begin{array}{ccc}\mathrm{i}& \mathrm{j}& \mathrm{k}\\ 2& -6& -3\\ 4& 3& -1\end{array}\right| \\ =\mathrm{i}(6+9)-\mathrm{j}(-2+12)+\mathrm{k}(6+24) \\ =15\mathrm{i}-10\mathrm{j}+30\mathrm{k} \\ =5(3\mathrm{i}-2\mathrm{j}+6\mathrm{k}) \\ |\overline{\mathrm{a}}\times \overline{\mathrm{b}}|=5\sqrt{9+4+36}=5\times 7 \\ \mathrm{Unit} \mathrm{vector}=\frac{3\mathrm{i}-2\mathrm{j}+6\mathrm{k}}{7} \end{gathered}$$