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📰 \boxed{p = 2, \, q = 2, \, r = 6} 📰 \]Question: A tech entrepreneur in Athens designs a drone navigation system where the drone's path is represented by unit vectors $\mathbf{u}$ and $\mathbf{v}$ with an angle $\theta$ between them. If $\mathbf{u} \cdot \mathbf{v} = \frac{\sqrt{3}}{2}$, find $\theta$. 📰 Solution: The dot product of two unit vectors is $\mathbf{u} \cdot \mathbf{v} = \cos\theta$. Given $\cos\theta = \frac{\sqrt{3}}{2}$, the angle $\theta$ satisfies $\theta = \arccos\left(\frac{\sqrt{3}}{2}\right)$. This corresponds to $\theta = 30^\circ$ or $\frac{\pi}{6}$ radians. However, since cosine is positive in both the first and fourth quadrants, but angles between vectors are typically taken in $[0, \pi]$, the solution is $\boxed{\dfrac{\pi}{6}}$. 📰 Transform Your Ride These Lowrider Bikes Are Taking Hells By Storm 970455 📰 Secrets Of Java Bitwise Operators Revealed Speed Up Your Code Like A Pro 6580956 📰 The Wildest Super Mario Bros Show Ever Timeless Fun That Will Blow Your Mind 2105749 📰 Doggos Going Viral How Dogs Dow Ist Changing Canine Culture Forever 6063278 📰 Nyse Umc Insider Move Thats Taking Wall Street By Storm Dont Miss Out 6256292 📰 Signs Your Well Water Is Making You Sick 3590443 📰 Mcdonalds Logo 2569730 📰 This Secure System Will Save You Thousandsdont Miss The Ultimate Cybersecurity Secrets 8523513 📰 Senran Kagura Shinovi 356988 📰 From Fidelity Overland Park To Earning Local Heart Heres Why Its Popularity Soars 2661731 📰 Excel Hacks Turn Numbers Into Text In Seconds For Busy Professionals 3887658 📰 Cd Rates June 19 2025 5910607 📰 City Of Madelia 8412900 📰 From Infamy To Fame The Mind Blowing Story Behind Mankalah Explained 4947169 📰 From Betrayal To Revenge In Nikita Tv Seriesevery Episode Is Pure Drama Magic 3275651