Online visualization tool for planes (spans in linear algebra)

A great site is GeoGebra. It starts in 2D by default, but you can click on a settings button on the right to open a 3D viewer. You can add a point anywhere on the page then double-click it to set its coördinates. There are many tools, including drawing the plane determined by three given points. One of the pleasures of this site is that you can drag any of the points and it will dynamically adjust the objects you have created (so dragging a point will move the corresponding plane).

Here is a screenshot of the plane through $(3,0,0),(0,2,0)$, and $(0,0,4)$:

$\hskip2cm$

Relaxing the online restriction, I quite like Grapher (for macOS). For example, here is a plot of two planes, the plane in Théophile's answer and the plane $z = 0$, and of the three given points:

You should checkout CPM_3D_Plotter.
It runs in the browser, therefore you don't have to download or install any programs.
Because it is browser-based, it is also platform independent.
The user-interface is very clean and simple to use: