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"Want to Find Your Illinois Location in 60 Seconds? Here’s the County Map You Need! - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \sqrt{\left(1 - 0\right)^2 + \left(1 - 0\right)^2 + \left(1 - 0\right)^2} = \sqrt{3}

📌 Not 1, but symmetry suggests closest integer: \((1, 1, 1)\).

📌 Thus, the coordinates of the fourth vertex are:

📌 \boxed{(1, 1, 1)}

📌 Question:** An entomologist is analyzing the orthogonality of vectors representing insect flight paths. Find \(x\) such that the vectors \(\begin{pmatrix} 2 \\ 3 \\ x \end{pmatrix}\) and \(\begin{pmatrix} -1 \\ 4 \\ 2 \end{pmatrix}\) are orthogonal.

📌 \begin{pmatrix} 2 \\ 3 \\ x \end{pmatrix} \cdot \begin{pmatrix} -1 \\ 4 \\ 2 \end{pmatrix} = 2(-1) + 3(4) + x(2)

📌 + 12 + 2x = 0

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