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I have 2 points different points in 3D space $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$. These are not on the origin. It creates a vector and I would like to define the angle between this vector and normal vector of the plane laid down on the $X$-$Y$ plane.

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  • $\begingroup$ Basically what is your question here $\endgroup$ – Vedant Chourey May 13 at 14:20
  • $\begingroup$ my question is how to define this angle. $\endgroup$ – agenel May 13 at 14:52
  • $\begingroup$ The answer is given $\endgroup$ – Vedant Chourey May 13 at 14:53
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Assuming define means determine the angle, viewing this vector as a true length looking on the edge of the $X$-$Y$ plane, the angle $L$ between the vector and the plane is:

$$L = \arctan(\frac{z_2 - z_1}{\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}})$$

The angle to the normal vector is therefore $90 - L$.

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