I know the coordinates of 2 points (x1,y1,z1) and (x2,y2,z2) which define a line in 3D space. I would like to find the location of a third point (x3,y3,z3) along this line which is a known distance R13 from point 1 and distance R23 from point 2.

I am a little stumped on how to get started. I think I have to use the parametric form for the line, x=x1+(x2-x1)t, y=y1+(y2-y1)t, z=(z2-z1)t, and the fact that R23^2=(x2-x3)^2 + (y2-y3)^2 + (z2-z3)^2, R13^2=(x1-x3)^2 + (y1-y3)^2 + (z1-z3)^2. But I am not sure how to set up the equations and solve them to get (x3,y3,z3) since I haven't worked with the parametric form before. Any help is appreciated.