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Home » 0,1,3 → valid - Esdistancia

0,1,3 → valid - Esdistancia

📅 March 17, 2026 👤 scraface

Mar 17, 2026

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📌 الإجابة النهائية:** الزوايا هي $\boxed{240^\circ}$ و $\boxed{300^\circ}$.

📌 السؤال: أوجد المتجه $\mathbf{v}$ بحيث أن $\mathbf{v} \times \begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix} = \begin{pmatrix} 0 \\ 3 \\ -2 \end{pmatrix}$.

📌 الحل: ليكن $\mathbf{v} = \begin{pmatrix} v_1 \\ v_2 \\ v_3 \end{pmatrix}$. حاصل الضرب التقاطعي هو:

📌 \mathbf{v} \times \begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix} = \begin{pmatrix} 0 \cdot 0 - v_3 \cdot 0 \\ v_3 \cdot 1 - v_1 \cdot 0 \\ v_1 \cdot 0 - v_2 \cdot 1 \end{pmatrix} = \begin{pmatrix} 0 \\ v_3 \\ -v_2 \end{pmatrix}

📌 نحتاج إلى أنه يساوي $\begin{pmatrix} 0 \\ 3 \\ -2 \end{pmatrix}$, مما يعطي:

📌 v_3 = 3 \\

📌 -v_2 = -2 \implies v_2 = 2

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