Vector Algebra

The vectors $\bar{a}, \bar{b}$ and $\bar{c}$ are such that $|\overline{\mathrm{a}}|=2,|\overline{\mathrm{~b}}|=4,|\overline{\mathrm{c}}|=4$. If the projection of $\overline{\mathrm{b}}$ on $\overline{\mathrm{a}}$ is equal to projection of $\overline{\mathrm{c}}$ on $\overline{\mathrm{a}}$ and $\overline{\mathrm{b}}$ is perpendicular to $\overline{\mathrm{c}}$, then the value of $|\overline{\mathrm{a}}+\overline{\mathrm{b}}-\overline{\mathrm{c}}|$ is