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Home » ## Marated關鍵词标注 — Episode Highlights - Midis

## Marated關鍵词标注 — Episode Highlights - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 \boxed{240^\circ} \quad \text{و} \quad \boxed{300^\circ}

📌 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 \\

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