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📰 Let me write the first question: 📰 Question: Find the vector $\mathbf{v}$ that satisfies $\mathbf{v} \times \mathbf{w} = \mathbf{p}$, where $\mathbf{w} = \begin{pmatrix} 2 \\ -1 \\ 3 \end{pmatrix}$ represents wind velocity and $\mathbf{p} = \begin{pmatrix} 5 \\ 0 \\ -2 \end{pmatrix}$ models the pollination force vector. 📰 Solution: To solve for $\mathbf{v}$, we use the cross product equation $\mathbf{v} \times \mathbf{w} = \mathbf{p}$. Let $\mathbf{v} = \begin{pmatrix} v_1 \\ v_2 \\ v_3 \end{pmatrix}$. The cross product $\mathbf{v} \times \mathbf{w}$ is calculated as $\begin{pmatrix} v_2 \cdot 3 - v_3 \cdot (-1) \\ v_3 \cdot 2 - v_1 \cdot 3 \\ v_1 \cdot (-1) - v_2 \cdot 2 \end{pmatrix} = \begin{pmatrix} 3v_2 + v_3 \\ 2v_3 - 3v_1 \\ -v_1 - 2v_2 \end{pmatrix}$. Setting this equal to $\mathbf{p} = \begin{pmatrix} 5 \\ 0 \\ -2 \end{pmatrix}$, we get the system: 📰 C U S C U T A 9619333 📰 Discover The Scruff App The Revolutionary Tool That Changes How You Scrub Your Routine Forever 1853688 📰 Taskbar Wont Hide Heres Why Your Pc 4579025 📰 Visa Waiver Program 5063526 📰 Henrys End Brooklyn Ny 2565464 📰 No Ire Is Your Secret Weapon Discover Why You Never Should Get Angry Again 9489106 📰 Crazy Racing Games That Will Make You Scream Believe What Youre About To See 8051071 📰 Rodeohouston 2880930 📰 Mexico Cancun Hotel Iberostar 9733586 📰 Tanoor Sammamish 8019079 📰 5 Inside The Bewildering Paintball Game Hunt That Launching Viral Memes 9561462 📰 Unlock The Secret Why Qualified Dividends Tax Rate Is Lower Than You Thought 1057405 📰 Kew Gardens 3802191 📰 Microsoft Picture Editor Windows 10 1002244 📰 Abbasid Empire 5808577