A vector $\overline{\mathrm{c}}$  of magnitude $\sqrt{7}$  which is perpendicular to the vector $\overline{\mathrm{a}}=2\overline{\mathrm{j}}-\overline{\mathrm{k}}$  and  $\overline{\mathrm{b}}=-\overline{\mathrm{i}}+2\overline{\mathrm{j}}-3\overline{\mathrm{k}}$ and makes an obtuse angle with the y -axis is given by

$\begin{array}{l}\overline{\mathrm{c}}\perp \overline{\mathrm{a}} , \overline{\mathrm{c}}\perp \overline{\mathrm{b}} \\ \overline{\mathrm{c}}=\mathrm{\lambda }(\overline{\mathrm{a}}\times \overline{\mathrm{b}})\\ \overline{\mathrm{c}}=\mathrm{\lambda }\left|\begin{array}{ccc}\overline{\mathrm{i}}& \overline{\mathrm{j}}& \overline{\mathrm{k}}\\ 0& 2& -1\\ -1& 2& -3\end{array}\right|=\mathrm{\lambda }(-4\overline{\mathrm{i}}+\overline{\mathrm{j}}+2\overline{\mathrm{k}})\Rightarrow \left|\overline{\mathrm{c}}\right|=\sqrt{16{\mathrm{\lambda }}^2+{\mathrm{\lambda }}^2+4{\mathrm{\lambda }}^2}\\ \Rightarrow \sqrt{16{\mathrm{\lambda }}^2+{\mathrm{\lambda }}^2+4{\mathrm{\lambda }}^2}=\sqrt{7}\\ \sqrt{21{\mathrm{\lambda }}^2}=\sqrt{7}\Rightarrow \mathrm{\lambda }=\pm \frac{1}{3}\\ \overline{\mathrm{c}}\cdot \overline{\mathrm{y}}=|\overline{\mathrm{c}}\parallel \overline{\mathrm{y}}|\cos \mathrm{\alpha }<0\Rightarrow \left(\pm \frac{1}{\sqrt{3}}\times 1\right)<0\\ \Rightarrow \mathrm{\lambda }=-\frac{1}{\sqrt{3}}\\ \overline{c}=\frac{1}{\sqrt{3}}(4\overline{\mathrm{i}}-\overline{\mathrm{j}}-2\overline{\mathrm{k}})\end{array}$