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📰 Question: Find the value of \(x\) such that the vectors \(\begin{pmatrix} x \\ 2 \\ -1 \end{pmatrix}\) and \(\begin{pmatrix} 3 \\ -1 \\ 4 \end{pmatrix}\) are orthogonal. 📰 Solution: Two vectors are orthogonal if their dot product is zero. Compute the dot product: \(3x + (2)(-1) + (-1)(4) = 3x - 2 - 4 = 3x - 6\). Set this equal to zero: \(3x - 6 = 0 \implies x = 2\). 📰 Question: Find the vector \(\mathbf{v} = \begin{pmatrix} a \\ b \\ c \end{pmatrix}\) such that \(\mathbf{v} \times \begin{pmatrix} 2 \\ -1 \\ 3 \end{pmatrix} = \begin{pmatrix} 5 \\ 7 \\ -4 \end{pmatrix}\). 📰 Learn Piano Faster Than Ever With The Top Ipad Appsee How Now 2615835 📰 The Game Net Worth 1711332 📰 Youll Never Beat This Hack Gameheres The Ultra Secret Code 2775351 📰 Unlock Your Hidden Fate The Astrologer Bot Whispers Your Exact Path 7611295 📰 Millbrae Pancake House 3586124 📰 Kxan Weather Radar Captures Mystery Thunder Sea That Throws Us Into Chaos 3810115 📰 The Inside Scoop On Mesoblast Stock Its Poised For A Massive Jumpdont Sleep 9998629 📰 Food For Less Top 10 Budget Bites You Wont Want To Stop Eating 890553 📰 Calculate The Revenue From Type A Gadgets 49282 📰 The Ultimate Camisa Rescue Looks So Good Youll Forget You Ever Wore Anything Else 6855111 📰 Youre Missing This Secret The Ultimate Ytm Calculator That Boosts Your Investments Overnight 2212306 📰 Win 10 Enterprise Download 1672112 📰 Wells Fargo Business Account Promotion 6594291 📰 Judge Doom Roger Rabbit 4662544 📰 Why Everyones Obsessed With Rathian The Hidden Power Inside 3178425