Direction cosines by computer

You will write three small functions: one that finds the direction ratios of the line through two points, one that turns direction ratios into direction cosines, and one that tests whether three numbers can be direction cosines.

The idea. The direction ratios of the line from $P$ to $Q$ are the differences of the coordinates. Dividing them by the length $\sqrt{a^2 + b^2 + c^2}$ gives the direction cosines. A set of direction cosines must have squares that add to $1$.

Your tasks.

1. Finish direction_ratios(p, q). Return the three differences $q - p$ as a tuple.
2. Finish direction_cosines(a, b, c). Divide each ratio by the length.
3. Finish is_direction_cosines(l, m, n). Return True when $l^2 + m^2 + n^2$ is within 1e-9 of $1$.