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Home » "Star Wars 7 Dark Secret Revealed: Is This the Epic You’ve Been Waiting For?] - Abbey Badges

"Star Wars 7 Dark Secret Revealed: Is This the Epic You’ve Been Waiting For?] - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 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

📌 Solving for \(x\):

📌 2x = -10 \quad \Rightarrow \quad x = -5

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