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Home » \[ w \times 3w = 192 \] - Tacotoon

\[ w \times 3w = 192 \] - Tacotoon

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 An anthropologist is studying the cultural significance of ancient structures that align with celestial bodies. They model the direction vector of a sunrise alignment as \(egin{pmatrix} 3 \ 4 \end{pmatrix}\) and need to find a perpendicular direction vector for a shadow alignment. Find \(x\) so that the vectors \(egin{pmatrix} 3 \ 4 \end{pmatrix}\) and \(egin{pmatrix} x \ -6 \end{pmatrix}\) are orthogonal.

📌 Two vectors \(egin{pmatrix} a \ b \end{pmatrix}\) and \(egin{pmatrix} c \ d \end{pmatrix}\) are orthogonal if their dot product is zero: \(a \cdot c + b \cdot d = 0\).

📌 Given vectors:

📌 egin{pmatrix} 3 \ 4 \end{pmatrix} \quad ext{and} \quad egin{pmatrix} x \ -6 \end{pmatrix}

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