3d Geometry

Let \(\mathrm{Q}\) and \(\mathrm{R}\) be the feet of perpendiculars from the point \(\mathrm{P}(a, a, a)\) on the lines \(x=y, z=1\) and \(x=-y, z=-1\) respectively. If \(\angle \mathrm{QPR}\) is a right angle, then \(12 a^2\) is equal to _________.