Question

Is there a point slope form for a three dimensional line?

Answer 1

Not really, but...

Explanation:

Something vaguely similar that you can use for a line in any number of dimensions is a point-vector form, which you could write like this:

`underline(x) = underline(x_0)+tvec(v)`

In three dimensions:

`(x, y, z) = (x_0, y_0, z_0) + t(u, v, w)`

`= (x_0 + tu, y_0 + tv, z_0 + tw)`

where `(x_0, y_0, z_0)` is a point through which the line passes, `(u, v, w)` is a vector describing the direction of the line and `t` is a parameter ranging over `RR`.

If `(u, v, w)` (or in more generality `vec(v)`) is of unit length, then the parameter `t` acquires extra meaning in being the distance along the line from the fixed point.