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which character are you in stranger things - AssociationVoting

📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 5**Question:** A futuristic AI device outputs a vector in 3D space that must be orthogonal to both eigenvector $\begin{pmatrix} 1 \\ -2 \\ 3 \end{pmatrix}$ and $\begin{pmatrix} 4 \\ 0 \\ -1 \end{pmatrix}$. What vector satisfies this condition?

📌 Solution: To find a vector orthogonal to both, compute their cross product:

📌 \begin{pmatrix} 1 \\ -2 \\ 3 \end{pmatrix} \times \begin{pmatrix} 4 \\ 0 \\ -1 \end{pmatrix} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 1 & -2 & 3 \\ 4 & 0 & -1 \end{vmatrix}

📌 = \mathbf{i}((-2)(-1) - (3)(0)) - \mathbf{j}((1)(-1) - (3)(4)) + \mathbf{k}((1)(0) - (-2)(4))

📌 = \mathbf{i}(2) - \mathbf{j}(-1 - 12) + \mathbf{k}(0 + 8) = 2\mathbf{i} + 13\mathbf{j} + 8\mathbf{k}

📌 Thus, the vector is $\boxed{\begin{pmatrix} 2 \\ 13 \\ 8 \end{pmatrix}}$.

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