I have a plane with equation 3x + 2y + 5z - 19 = 0. With the help of Python/MatPlotlib, I could draw this plane also. Please find the image below.
What I would like to know is how to determine the angle of this plane?
2026-03-27 12:20:11.1774614011
How can I find the angle of the surface/3D Plane.
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The normal vector to the plane is $n=(3,2,5)$, from that we can find the angles we are interested in using dot product.
For example the angle for the normal with $x-y$ plane, with normal $e_3=(0,0,1)$ is given by
$$\cos \theta=\frac{n\cdot e_3}{|n||e_3|}=\frac{5}{\sqrt{28}}$$