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Home » From Embarrassment to November Chaos: Our Top Picks for Christmas Ugly Jumpers - AMAZONAWS

From Embarrassment to November Chaos: Our Top Picks for Christmas Ugly Jumpers - AMAZONAWS

📅 March 6, 2026 👤 scraface

Mar 06, 2026

From Embarrassment to November Chaos: Our Top Picks for Christmas Ugly Jumpers

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📌 Solution: The given points lie on the plane \(z = 3\). The vector from \((1, 2, 3)\) to \((1, 5, 3)\) is \((0, 3, 0)\), and the vector to \((4, 2, 3)\) is \((3, 0, 0)\). The fourth vertex on the same face is obtained by adding these vectors: \((1 + 3, 2 + 3, 3) = (4, 5, 3)\).

📌 Solution: Two vectors are orthogonal if their dot product is zero. Compute the dot product: \(3x + (2)(-1) + (-1)(4) = 3x - 2 - 4 = 3x - 6\). Set this equal to zero: \(3x - 6 = 0 \implies x = 2\).

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📌 Therefore, the number of permutations satisfying both conditions is:

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