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📰 Question: If \(\mathbf{u}\), \(\mathbf{v}\), and \(\mathbf{w}\) are unit vectors, find the maximum value of \(\mathbf{u} \cdot (\mathbf{v} + \mathbf{w})\). 📰 Solution: The dot product \(\mathbf{u} \cdot (\mathbf{v} + \mathbf{w}) = \mathbf{u} \cdot \mathbf{v} + \mathbf{u} \cdot \mathbf{w}\). Since \(\mathbf{u}\), \(\mathbf{v}\), and \(\mathbf{w}\) are unit vectors, each dot product is at most 1. The maximum occurs when \(\mathbf{u}\) aligns with both \(\mathbf{v}\) and \(\mathbf{w}\), i.e., \(\mathbf{v} = \mathbf{w} = \mathbf{u}\). Then \(\mathbf{u} \cdot (\mathbf{v} + \mathbf{w}) = 1 + 1 = 2\). 📰 \boxed{2}Question: What is the smallest four-digit number that is a multiple of the least common multiple of the numbers $12$ and $18$, and also divisible by the square of the smallest prime greater than $10$? 📰 Unlock Massive Rows Why This Lat Pull Down Must Be In Your Routine 5000365 📰 Frank Oceans Secret Message In Chancel Lyricsclick To Discover The Controversial Truth 9137617 📰 The Ultimate Cmcm Punk Collection That Shook The Scenewatch Your Jaw Drop 6844625 📰 Solaris Operating System 6403954 📰 Stop Clutter Uninstall Programs On Windows 7 In Just 5 Minutes 5167215 📰 The Circumference Is Given By 2Pi R 314 6877819 📰 You Wont Believe What Hidden Lures Hide Behind Your Carefirst Sign In 2471858 📰 Race Street Cafe 9934579 📰 Grand Canyon Hotels South Rim 1522999 📰 Kohls Shock Massive Closures Sweep The Nationwatch Whats Vanishing First 4817511 📰 Master Your Workflow How Process Monitor Microsoft Transforms System Monitoring 3605069 📰 Hyper Rare Air 4S Leakedinside The Unseen Features That Shock Fans 4758190 📰 Your Racepass Secrets Are Inside How Myracepass Changes Everything 3729630 📰 Historial 8165537 📰 Jimmy Neutron Characters 4442215