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📰 Solution: Let $\theta$ be the angle between any pair of vectors. Since $\mathbf{u} \cdot \mathbf{v} = \cos\theta = \frac{1}{2}$, $\theta = 60^\circ$. The magnitude squared is $|\mathbf{u} + \mathbf{v} + \mathbf{w}|^2 = 3 + 2(\mathbf{u} \cdot \mathbf{v} + \mathbf{u} \cdot \mathbf{w} + \mathbf{v} \cdot \mathbf{w}) = 3 + 2(3 \cdot \frac{1}{2}) = 3 + 3 = 6$. Thus, the maximum value is $\sqrt{6}$. 📰 Question: A plant biologist studies stress responses using vectors $\begin{pmatrix} 1 \\ x \\ 2 \end{pmatrix}$ and $\begin{pmatrix} x \\ 3 \\ -1 \end{pmatrix}$. Find $x$ such that the vectors are orthogonal. 📰 Solution: For orthogonality, their dot product must be zero: $1 \cdot x + x \cdot 3 + 2 \cdot (-1) = 0$. Simplifying, $x + 3x - 2 = 0 \Rightarrow 4x = 2 \Rightarrow x = \frac{1}{2}$. 📰 A Car Travels At A Constant Speed Of 60 Miles Per Hour If It Starts Its Journey At 900 Am And Arrives At Its Destination At 300 Pm How Far Did It Travel 1891637 📰 Download Your Files In Secondsuse This Super Speed Download Time Calculator 5399143 📰 How To Redo In Excel Like A Prono More Mistakes 4310080 📰 Water Gushing Back The Shocking Plunger Trick You Must Watch Now 5735528 📰 Perimeter 2Length Width 23X X 8X 48 5129955 📰 Wheres Your Money Going Stock Market Heatmap Breaks Down The Hotstocks Right Now 4774950 📰 Stop Waste Timeget Your Medical Records Fast With This Easy Step By Step Guide 9640049 📰 Bun Test 4461927 📰 You Wont Believe Which New England Town Has Secrets No One Knows About 2237078 📰 Share A Onedrive Folder Todaythis Simple Trick Gets It Done Fast 9841365 📰 Heidi Klum Movies And Tv Shows 640613 📰 You Wont Believe Where You Can Stream Pokmon Without Paying A Dime 7064698 📰 Watch Whiplash 997497 📰 You Wont Believe What Happened When Your Car Stopped Cold 6607576 📰 Bronzong Weakness Exposed The Deadly Flaw You Cant Ignore In 2024 8543476