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Home » Lost My Patience: Stop Being a Horrible Grandpa or Lose Me Forever! - Aurero

Lost My Patience: Stop Being a Horrible Grandpa or Lose Me Forever! - Aurero

📅 March 15, 2026 👤 scraface

Mar 15, 2026

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📌 Let \(\mathbf{v} = egin{pmatrix} x \ y \ z \end{pmatrix}\), \(\mathbf{a} = egin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}\), and \(\mathbf{v} imes \mathbf{a} = egin{pmatrix} 0 \ 0 \ 5 \end{pmatrix}\).

📌 \mathbf{v} imes \mathbf{a} = egin{vmatrix}

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

📌 = egin{pmatrix} 3y - 2z \ - (3x - z) \ 2x - y \end{pmatrix} = egin{pmatrix} 3y - 2z \ -3x + z \ 2x - y \end{pmatrix}

📌 Set equal to \(egin{pmatrix} 0 \ 0 \ 5 \end{pmatrix}\):

📌 3y - 2z = 0 \

📌 -3x + z = 0 \

📌 2x - y = 5

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