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How to find the angle between two 3D lines

I’ve got the following lines, which are generated by two 2D lines. The two lines intersect at (0,0,0).

I’m trying to figure out how to calculate the angle that I’m looking for. In this case, the angle is 32.2 degrees.
Can anyone help?

A:

In plain English the equation is
\[\frac{((x_1-x_2)x_3 +(y_1-y_2)y_3)}{\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}}\]
The square root of the quotient of two perpendicular variables is “the cosine of the angle”.
The remainder after division by the equation of a line in $3$d is the normal vector of the plane that it defines. If this is the upper hemisphere $z>0$, then the normal vector is $(1,\,0,\,0)$ so the angle $\theta$ is $90^\circ-\tan^{ -1}\frac{y_2}{x_2}$

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