Holding Down a Balloon

Problem: A tethered balloon is held by three ropes tied to a ring at the origin. The ropes run toward ground anchors along the directions \(\{3\,\mathbf{i} - 4\,\mathbf{k}\}\), \(\{-2\,\mathbf{i} + 3\,\mathbf{j} - 4\,\mathbf{k}\}\) and \(\{-2\,\mathbf{i} - 3\,\mathbf{j} - 4\,\mathbf{k}\}\). The resultant of the three rope tensions must be 4.5 kN straight down. Find the three tensions.