New theoretical Ne vi] electron density-sensitive ratios are presented for the intercombination transitions R1 = 1(1006.1 A)/I(999.6 A) and R2 = 1(1010.6 A)/I(999.6 A). Temperature-sensitive ratios are also given for the Ne v] ratio R = 1(1137.0 A)/I(1574.8 A). We discuss the potential usefulness of these line ratios for studying hot gas and apply them to the case of the symbiotic system RR Telescopii. Using far-UV data that has recently been acquired with the Hopkins Ultraviolet Telescope, we conclude that the Ne V and Ne vi emission in RR Tel is due to photoionization, with the temperature and density of the emitting region being approximately T _ 18000 K and Ne 106 cm 3, respectively. These results are similar to those estimated using other high ionization line diagnostics of the nebular material, such as 0 V 1(1371 A)/I(1644 A) and Ne iv] 1(1602 A)/I(2423 A). Although these Ne v] and Ne vi] lines have been used as diagnostics for solar physics, we believe that this is the first instance in which they have been applied to another astrophysical object. Subject headings: atomic processes binaries: symbiotic stars: individual (RR Telescopii) ultraviolet: stars ; PUBLISHED