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📰 Solution: Let $ \vec{OA} = \mathbf{a} $, $ \vec{OB} = \mathbf{b} $. Then $ \overrightarrow{OC} = m\mathbf{a} + n\mathbf{b} $. For $ \overrightarrow{OC} \perp (\mathbf{a} - \mathbf{b}) $, their dot product is zero: $ (m\mathbf{a} + n\mathbf{b}) \cdot (\mathbf{a} - \mathbf{b}) = 0 $. Expand: $ m\|\mathbf{a}\|^2 - m\mathbf{a} \cdot \mathbf{b} + n\mathbf{b} \cdot \mathbf{a} - n\|\mathbf{b}\|^2 = 0 $. Substitute $ \|\mathbf{a}\| = 2 $, $ \|\mathbf{b}\| = 3 $, $ \mathbf{a} \cdot \mathbf{b} = 2 \cdot 3 \cdot \cos 60^\circ = 3 $: $ 4m - 3m + 3n - 9n = 0 \Rightarrow m - 6n = 0 $. Choose $ n = 1 $, then $ m = 6 $. Normalize if needed, but the relation is $ m = 6n $. For simplicity, take $ n = 1 $, $ m = 6 $. 📰 \boxed{(6, 1)}Question: A hydrologist studying groundwater flow measures the volume of water (in liters) passing through a sensor at different times, recording values that are positive multiples of 5. If the cube of one such measurement is less than 1500, what is the greatest possible value of that measurement? 📰 Solution: Let the measurement be $ u $, a positive multiple of 5 such that $ u^3 < 1500 $. 📰 Final Weight 05 2 05 32 160 Grams 8383112 📰 Gurren Topping Secrets You Wont Believe What This Legend Can Do 2724281 📰 You Wont Believe What Happened After You Used The Nike Res Registryunlock Exclusive Perks 1654970 📰 Unlock The Secrets The Perfect Nbis Message Board For Cutting Edge Community Talks 6708376 📰 Spartan Armor The Secret Weapon That Appliance Store Sold Giants 7977069 📰 Barcelona Left Reeling As Valladolid Bursts Onto The Scene With Fire And Fury 5083530 📰 You Wont Believe What Happens When The Full Moon Triggers The Howl Werewolf Transformation 2108103 📰 Log Out Fidelity Nowyoull Get Unlocked Access To Hidden Features You Didnt Know About 1608729 📰 These Strawberry Plants Are Selling Faster Than Anyone Expecteddont Miss Out 3375119 📰 Hrtbrkr Finally Explained The Mind Bending Code Coding This App Abuse 929504 📰 You Wont Believe What Happened When She Bit Into The Biscuite It Changed Her Life Forever 9517945 📰 The Shocking Carnivore Secrets You Were Never Told 2032780 📰 Approximately X Approx 627 Or X Approx 127 933163 📰 How To Change Screen Icon Size 4713181 📰 Best Credit Card For International 4724827