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Discover Every City in Italy—Click to See the Complete Map of Iconic Destinations! - Get link 4share

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 \mathbf{u} \cdot \mathbf{v} = 3(-1) + 4(2) = -3 + 8 = 5

📌 Next, find the magnitudes of $\mathbf{u}$ and $\mathbf{v}$:

📌 \|\mathbf{u}\| = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5

📌 \|\mathbf{v}\| = \sqrt{(-1)^2 + 2^2} = \sqrt{1 + 4} = \sqrt{5}

📌 Now, substitute these into the formula:

📌 = 5 \cdot \sqrt{5} \cdot \cos \theta

📌 Solve for $\cos \theta$:

📌 \cos \theta = \frac{5}{5 \cdot \sqrt{5}} = \frac{1}{\sqrt{5}} = \frac{\sqrt{5}}{5}

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