I am trying to understand how the following identity in homogeneous coordinates comes about and how to visualise the two multiplying parts P and l in the 3d cartesian coordinates. Are they orthogonal to each other in order for the dot product to be 0. Can you show it in a picture?

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My understanding is shown in the picture below.

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More background can be found here:

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  • $\begingroup$ Equation (5) in the reference you provided shows exactly what you are looking for. $\endgroup$ – Théophile Feb 5 at 13:41
  • $\begingroup$ In the future, please take the time to enter important parts of your question as text instead of linking to pictures of it. Images are neither searchable nor accessible to screen readers, nor do they show up in summaries. You can find a quick reference for formatting mathematical expressions in MathJax here. $\endgroup$ – amd Feb 5 at 21:38
  • $\begingroup$ Hint: Consider points and lines in $\mathbb R^3$ that are on the plane $z=1$ instead of on the $x$-$y$ plane. $\endgroup$ – amd Feb 5 at 21:39

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