Hello!

Q: With respect to an origin O, the points P and Q have position vectorspandqrespectively, given byp= (cos t)i+ (sin t)j-k,q= (cos 2t)i- (sin 2t)j+ $\displaystyle \frac{1}{2}$k, where t is a real parameter such that 0 < t < $\displaystyle 2\pi$. Given thatp$\displaystyle \cdot $q= cos 3t - $\displaystyle \frac{1}{2}$, hence or otherwise, find the greatest value of angle POQ.

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