My cat is standing on the plane 3x+2y+z = 4. Its head is at (0,-1,-8) and the tip of its tail is at (-4,-6,-2). 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.
