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## Homework Statement

Within the xy-plane, two vectors having lengths P and Q rotate around the z-axis with angular velocities ω and –ω. At t = 0,these vectors have orientations with respect to the x axis specified by θ1 and θ2. How do I find the orientation of the major axis of the resulting ellipse relative to the x-axis.

## The Attempt at a Solution

P=|p|cos(θ1+ωt) x^+ |p|sin(θ1+ωt) y^

Q=|q|cos(θ1+ωt) x^+ |q|sin(θ1+ωt) y^

x^- x hat

y^-y hat

How do I solve this after these 2 equations?

I tried to group the x and y vectors separately. But i could not figure out anything after that.

X= |p|cos(θ1+ωt)+|q|cos(θ1+ωt)

Y=|p|sin(θ1+ωt)+ |q|sin(θ1+ωt)

Without the θ terms I could have just squared both sides and added it. But now I am stuck. Thank you for the help :)