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📰 Question: In a city grid, $\|\overrightarrow{OA}\| = 5$ km and $\|\overrightarrow{OB}\| = 12$ km, with an angle of $90^\circ$ between them. If $\overrightarrow{OC} = 2\overrightarrow{OA} - \overrightarrow{OB}$, find $\|\overrightarrow{OC}\|$. 📰 Solution: Use the Pythagorean theorem since $\overrightarrow{OA}$ and $\overrightarrow{OB}$ are perpendicular. Compute $\|\overrightarrow{OC}\|^2 = (2\|\overrightarrow{OA}\|)^2 + (\|\overrightarrow{OB}\|)^2 = 4(25) + 144 = 100 + 144 = 244$. Thus, $\|\overrightarrow{OC}\| = \sqrt{244} = 2\sqrt{61}$. Final answer: $\boxed{2\sqrt{61}}$. 📰 Question: There exist constants $m$ and $n$ such that $\overrightarrow{OC} = m\overrightarrow{OA} + n\overrightarrow{OB}$, where $\overrightarrow{OA} = \begin{pmatrix} 1 \\ 2 \end{pmatrix}$, $\overrightarrow{OB} = \begin{pmatrix} -1 \\ 3 \end{pmatrix}$, and $\overrightarrow{OC} = \begin{pmatrix} 4 \\ 5 \end{pmatrix}$. Enter the ordered pair $(m, n)$. 📰 Natural 200 Times 082 200 Times 064 128 8277289 📰 Surprise How Black Mussels Are Dominating The Protein Crunch This Year 6413321 📰 The Lifetime App Doctors Wont Stop Recommendingsee How It Revolutionizes Your Daily Life 7550341 📰 Youtube Downloader Risk Free Discover The Safe Way To Save Videos Instantly 8612597 📰 Unlock Mind Blowing Sql Server Pivot Secrets Every Data Pro Must Know 5201976 📰 Watch The Chilean Peso To Usd Jumpexperts Predict Massive Gains 6344156 📰 For Each Final Matrix State The Solution 725635 📰 Paramount Shows 6996763 📰 Wacom Cintiq 13Hd Driver 7575384 📰 Cts Share Value Bombsexperts Say Its Just The Beginning 5183299 📰 Nintendo Switch 2 Games 9452834 📰 The Hidden Wat Stock Thats Surpassing Expectationsheres How To Jump In 6649763 📰 Define Rejoice 8039253 📰 Explore The Ultimate Cell City Tourhidden Wonders Inside Every Single Cell 3456389 📰 Why The Snow Market Cap Is Snowbalancing Global Investments Overnight 2643711