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📰 Solution: The angle $\theta$ between $\mathbf{a}$ and $\mathbf{b}$ is given by $\cos\theta = \frac{\mathbf{a} \cdot \mathbf{b}}{\|\mathbf{a}\| \|\mathbf{b}\|}$. Compute the dot product: $2(1) + (-3)(4) = 2 - 12 = -10$. Compute magnitudes: $\|\mathbf{a}\| = \sqrt{2^2 + (-3)^2} = \sqrt{13}$, $\|\mathbf{b}\| = \sqrt{1^2 + 4^2} = \sqrt{17}$. Thus, $\cos\theta = \frac{-10}{\sqrt{13}\sqrt{17}}$. Rationalizing, $\theta = \arccos\left(-\frac{10}{\sqrt{221}}\right)$. $\boxed{\arccos\left(-\dfrac{10}{\sqrt{221}}\right)}$ 📰 Question: If $\mathbf{u}, \mathbf{v}, \mathbf{w}$ are unit vectors in hydrology modeling, find the maximum value of $\mathbf{u} \cdot (\mathbf{v} \times \mathbf{w})$. 📰 Solution: The scalar triple product $\mathbf{u} \cdot (\mathbf{v} \times \mathbf{w})$ represents the volume of the parallelepiped formed by the vectors. Its maximum absolute value occurs when the vectors are mutually orthogonal. Since they are unit vectors, the maximum value is $1 \cdot 1 \cdot 1 = 1$. For example, if $\mathbf{u} = \mathbf{v} = \mathbf{w}$ are orthonormal, the 📰 Mtw Stock Insiders Are Buyingis This The Sign Of A Secret Bull Run 8456895 📰 Credit Cards For Business 3471285 📰 5 Saharan Tevas Nyse Rally Will This Trend Ignite Massive Profits Read Timely Insights Now 376741 📰 Fred Tasticores Secret Trick That Changed Everything Watch This Now 8083664 📰 Unlock Oracle Apex App Mastery Transform Your Business Today 9530205 📰 Dropped Phone In The Water 4596558 📰 Cazzo 6183784 📰 Pokmon Emerald Cheat Codes Exposed Beat Levels Faster With These Top Tips 9733302 📰 Watch Free Tv Shows 8667377 📰 Iowa Road Report 511 What Screenshot Shocked Drivers Everywhere 6712596 📰 Pinterest Earnings 6610001 📰 Epic Games Download Speed Slow 9154309 📰 Wet T Shirt Secret That Makes It Never Smell Again 1270236 📰 What Cliff Booth Never Said Benefits Will Change Your Life 4717754 📰 Sharon Credit Union Just Launched A Game Changing Savings Programdont Miss Out 3629459