My cat is standing on the plane 3x+2y+z = 4. Its head is at (0,-1,-3) and the tip of its tail is at \((-6,3,1)\) Measured from the plane, what is the difference between the height of my cat's head and my cat's tail? Enter your answer in the form $\frac{a \sqrt{b}}{c},$ where $a,$ $b,$ and $c$ are all positive integers.
