Let $\ddot{\mathrm{a}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\sqrt{2} \hat{\mathrm{k}}, \ddot{\mathrm{b}}=\mathrm{b}_1 \hat{\mathrm{i}}+\mathrm{b}_2 \hat{\mathrm{j}}+\sqrt{2} \hat{\mathrm{k}}$ and $\ddot{\mathrm{c}}=5 \hat{\mathrm{i}}+\hat{\mathrm{j}}+\sqrt{2} \hat{\mathrm{k}}$ be three vectors such that the projection vector of $\stackrel{a}{b}$ on $\stackrel{a}{a}$ is $\stackrel{n}{a}$. if $\stackrel{a}{a}+\stackrel{u}{b}$ is perpendicular to $\stackrel{n}{c}$, then $\stackrel{n}{b}$ is equal to:
