Finding rotation thetaR around the z axis? please help

Thelastmeheecaan

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Sep 13, 2019
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Hello, i'm working on an assignment for a company where i have to find the rotation ThetaR around the z axis. I have two vectors lets call them vector a and b
Known values are: phi-a, theta- a and phi-b and theta-b. As you can see in the picture i have to find the rotation around the z axis but i also have a tilt.
If i find the normal vector of these two vectors and compare this normal vector to the z axis i have my tilt as can be seen in the picture. But how do i now find theta R?
I know that x= sin (theta) x cos(phi) and y = sin (theta) x sin (theta) and z = cos(phi)
so the tilt can be calculated if you take the inner product of the two vectors with [ 0 0 1] which is de z- axis. XY view.pngXYZ view.png
 
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