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Home » Now, we use another identity for cubes: - DNSFLEX

Now, we use another identity for cubes: - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 2v_3 - 3v_1 = 0 \\

📌 -v_1 - 2v_2 = -2

📌 Revised 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 $\mathbf{p} = \begin{pmatrix} 3 \\ 0 \\ -2 \end{pmatrix}$ models the pollination force vector.

📌 Solution: Let $\mathbf{v} = \begin{pmatrix} v_1 \\ v_2 \\ v_3 \end{pmatrix}$. The cross product $\mathbf{v} \times \mathbf{w}$ is $\begin{pmatrix} 3v_2 + v_3 \\ 2v_3 - 3v_1 \\ -v_1 - 2v_2 \end{pmatrix} = \begin{pmatrix} 3 \\ 0 \\ -2 \end{pmatrix}$. This gives the system:

📌 3v_2 + v_3 = 3 \\

📌 From the second equation: $v_3 = \frac{3}{2}v_1$. From the third equation: $v_1 + 2v_2 = 2 \Rightarrow v_1 = 2 - 2v_2$. Substitute into the first equation: $3v_2 + \frac{3}{2}(2 - 2v_2) = 3 \Rightarrow 3v_2 + 3 - 3v_2 =

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