Find the projection of vector ( b + c ) on vector a, where a =2 i +2 j + k, b = i +3 j + k and c = i + k.

Find the projection of vector ( $\displaystyle \vec{\mathrm{b}}+\vec{\mathrm{c}}$ ) on vector $\displaystyle \vec{a}$, where $\displaystyle \vec{a}=2 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}$, $\displaystyle \overrightarrow{\mathrm{b}}=\hat{\mathrm{i}}+3 \hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $\displaystyle \overrightarrow{\mathrm{c}}=\hat{\mathrm{i}}+\hat{\mathrm{k}}$.