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Home » predominantly killer clickbait-style question titles: - Dyverse

predominantly killer clickbait-style question titles: - Dyverse

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Vectors are orthogonal if their dot product is zero:

📌 \mathbf{f} \cdot \mathbf{g} = 5(-1) + k(3) + 2(6) = -5 + 3k + 12 = 3k + 7 = 0

📌 Solve for $k$:

📌 3k = -7 \Rightarrow k = -\frac{7}{3}

📌 Thus, the required value is:

📌 \boxed{-\frac{7}{3}}

📌 ---Question: A bioinformatician is analyzing a dataset of DNA sequences, each represented as a point in a 3D space where each coordinate corresponds to the frequency of a nucleotide (A, C, G, T). If three such sequences correspond to the points $(1, 2, 3), (4, 5, 6),$ and $(7, 8, 9)$, find the coordinates of the fourth point that would form a regular tetrahedron with integer coordinates, ensuring all edges are of equal length.

📌 Solution: To find the fourth vertex of a regular tetrahedron with the given three vertices $A = (1, 2, 3)$, $B = (4, 5, 6)$, and $C = (7, 8, 9)$, we first compute the pairwise distances between the given points:

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