I need to find a point along a line segment in three-dimensional space, given two points.
For example: Find a point along a line segment between point $a(-2, -2, -2)$ and $b(3, 3, 3)$ which is at distance $3$ from point $a$, in the direction of point $b$.
I've been trying to figure out a way to do it with three parametric equations, or with similar triangles, but I can't seem to make sense of it.
Any help is greatly appreciated.