Finding a point on a 3d line I have two points in 3D which will create a single ray. I am trying to find a point on that ray which intersects a plane who's y coordinate is 0. So how do I find a point on a 3D line when I know the Y value already?


A generic point on the line can be written as $a+t(b-a)$, where $t$ is a real variable.
If you know a $y$ value (and $a,b$ have different $y$ values), you can find the point by determining the appropriate value of $t$.
In this case, you want to solve $a_y + t(b_y-a_y) = y_\text{given}$ for $t$. This gives
$t = \frac{y_\text{given}-a_y}{b_y-a_y}$, and then the point is given by $a+ t(b-a)$.
To find the point where the line intersects the $x-z$ plane, set  $y_\text{given} = 0$.
