The vector joining the points is \(\vec{PQ} = (-1, 0, -1)\), with magnitude \(\sqrt{1+0+1} = \sqrt{2}\). Normal to plane is \(\vec{n} = (1,1,1)\) with magnitude \(\sqrt{3}\). The component of \(\vec{PQ}\) perpendicular to plane is \(\frac{\vec{PQ} \cdot \vec{n}}{|\vec{n}|} = \frac{-1+0-1}{\sqrt{3}} = \frac{-2}{\sqrt{3}}\). Projection length = \(\sqrt{|\vec{PQ}|^2 - (\frac{\vec{PQ} \cdot \vec{n}}{|\vec{n}|})^2} = \sqrt{2 - \frac{4}{3}} = \sqrt{\frac{2}{3}}\).