Write the projection of the vector ( b + c ) on the vector a, where a = 2 i -2 j + k, b = i +2 j -2 k and c =2 i - j +4 k.

Write the projection of the vector $\displaystyle (\overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{c}})$ on the vector $\displaystyle \overrightarrow{\mathrm{a}}$, where $\displaystyle \overrightarrow{\mathrm{a}}=$ $\displaystyle 2 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\hat{\mathrm{k}}, \overrightarrow{\mathrm{b}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-2 \hat{\mathrm{k}}$ and $\displaystyle \overrightarrow{\mathrm{c}}=2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+4 \hat{\mathrm{k}}$.