I have two lines d1 has equation
x = 1 + t, y = 2 + t, z=3+t
and d2 has equation
x = 1 + 2t', y = 2  -3 t', z=3+t.
I know that, two this lines cut at the point P(1,2,3). By using 3dtools,

How can I input the line d1 in the form
like this

\path[3d/line with direction={(1,1,1) through (1,2,3) named d1}]
and

input the line d2 in the form
like this

\path[3d/line with direction={(2,-3,1) through (1,2,3) named d2}]

Is there command to find intersection of two lines d1 and d2? like this

\path[3d/intersection of={d1 with d2}] coordinate (I);

I want like this

\documentclass[tikz,border=3mm]{standalone}
\usepackage{tikz-3dplot}
\usetikzlibrary{3dtools,intersections}

\begin{document}
\tdplotsetmaincoords{70}{80}
\begin{tikzpicture}
\path
(1,2,3) coordinate (A);

\path[3d/line with direction={(1,1,1) through (A) named d1}];
\path[3d/line with direction={(2,-3,1) through (A) named d2}];
\path[3d/intersection of={d1 with d2}] coordinate (I);

\end{tikzpicture}
\end{document}

I added a routine for this to the [3dtools library](https://github.com/marmotghost/tikz-3dtools). The example you have is a bit special in that you define the two lines to run through the same point (which is why I had to add this case to the library). The computation follows [this post](https://math.stackexchange.com/a/271366).

\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{3dtools}% https://github.com/marmotghost/tikz-3dtools
\begin{document}
\begin{tikzpicture}[line cap=butt,line join=round,
3d/install view={phi=110,psi=0,theta=60}]
\path[3d/line with direction={(1,1,1) through (1,2,3) named d1},
3d/line with direction={(2,-3,1) through (1,2,3) named d2}];
\draw[red] (1,1,1) -- (1,2,3);
\draw[blue] (2,-3,1) -- (1,2,3);
\path[3d/intersection of={d1 with d2}] coordinate (I)
node[circle,fill,inner sep=0.5pt,
label=above:{$(I)=(\pgfmathparse{TD("(I)")}\pgfmathprintvector\pgfmathresult)$}]{};
\end{tikzpicture}
\end{document}

![Screen Shot 2020-11-20 at 9.58.14 PM.png](/image?hash=974d189f5e25b512f5463fd04eb0b05710251eea92026b5e79975f400e46253c)

Enter question or answer id or url (and optionally further answer ids/urls from the same question) from

Separate each id/url with a space. No need to list your own answers; they will be imported automatically.