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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 $\boxed{\dfrac{\pi}{6}}$. 📰 Dogs Pooping 7958784 📰 Barely Lethal 3326534 📰 Emergency Fund Amount 5769 📰 Secrets Unleashed How A High Profile Scandal Shook The Worlds Elite 6281762 📰 Alex Jones App 7223997 📰 76Ers Standings 8653199 📰 You Wont Believe How Simple This Photo Editor Isepic Results Guaranteed 6630953 📰 The King Of Staten Island 1014552 📰 Inn At The Presidio Hotel 5932719 📰 Unblocked Basketball Games 8310451 📰 Sql Oracle Trim 5896583 📰 Why This Newspaper Background Is Booming In Design Secrets Revealed 8209074 📰 The Hunter Within Rages Beneath The Moons Fierce Gaze 5133828 📰 Thrifty Car And Rental 1670964 📰 The Real Reason Subgirl0831 Took The Internet By Stormheres What Constituted The Truth 1924609