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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 $10$? 📰 Pictionary Generator 7228150 📰 Naked Gun From The Files Of Police Squad 9158297 📰 Colts 49Ers 451740 📰 Ken Williamson Referee 3616534 📰 Cash In Spanish 5639410 📰 Shocked By These Cbs Stocks Moves Could This Be Your Next Big Win 8037835 📰 Jobs In Houston 5708403 📰 The Shocking Truth Behind Chip Wildes Mind Blowing Past 9041746 📰 Microsoft Dynamics 365 Free Trial Unlock Premium Features Without Spending A Penny 5251278 📰 You Wont Believe How This Rockbot Learns To Battle Like A Legend 8482997 📰 Wells Fargo Bellaire Tx 629531 📰 Chargepoint Stock Price 3864232 📰 Unlock Epic Gorilla Tag Gameplay With These Must Have Mods 6403844 📰 Depot Fremont Ohio 7350703 📰 Alisa Reyes 6245198