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Home » You Won’t Believe What Yager Development Just Unleashed—Game Changer Inside! - Dachbleche24

You Won’t Believe What Yager Development Just Unleashed—Game Changer Inside! - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 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

📌 إذن، $\mathbf{v} = \begin{pmatrix} v_1 \\ 2 \\ 3 \end{pmatrix}$، حيث يمكن أن يكون $v_1$ أي عدد حقيقي لأنه لا يؤثر على الضرب التقاطعي مع $\begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix}$. للحصول على حل خاص، نضع $v_1 = 0$:

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