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Home » $ x + u = 2 $, $ y + v = 4 $, - 500apps

$ x + u = 2 $, $ y + v = 4 $, - 500apps

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 \mathbf{a} \times (\mathbf{v} \times \mathbf{a}) = \mathbf{a} \times \mathbf{b}

📌 Using the identity $ \mathbf{a} \times (\mathbf{v} \times \mathbf{a}) = (\mathbf{a} \cdot \mathbf{a})\mathbf{v} - (\mathbf{a} \cdot \mathbf{v})\mathbf{a} $, and since $ \mathbf{a} \cdot \mathbf{v} = 0 $, this becomes:

📌 \|\mathbf{a}\|^2 \mathbf{v} = \mathbf{a} \times \mathbf{b}

📌 Compute $ \|\mathbf{a}\|^2 = 1^2 + 2^2 + 3^2 = 1 + 4 + 9 = 14 $

📌 Now compute $ \mathbf{a} \times \mathbf{b} $:

📌 \mathbf{a} \times \mathbf{b} = \begin{vmatrix}

📌 & -2 & 1 \\

📌 \end{vmatrix} = \mathbf{i}(2 \cdot 1 - 3 \cdot (-2)) - \mathbf{j}(1 \cdot 1 - 3 \cdot 1) + \mathbf{k}(1 \cdot (-2) - 2 \cdot 1)

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