Vector Algebra

Let \(\overline{\mathrm{u}}, \overline{\mathrm{v}}\) and \(\overline{\mathrm{w}}\) be the vectors such that \(|\overline{\mathrm{u}}|=1; |\bar{v}|=2 ;|\bar{w}|=3\). If the projection of \(\bar{v}\) along \(\bar{u}\) is equal to that of \(\overline{\mathrm{w}}\) along \(\overline{\mathrm{u}}\) and \(\overline{\mathrm{v}}, \overline{\mathrm{w}}\) are perpendicular to each other, then \(|\bar{u}-\bar{v}+\bar{w}|\) is equal to