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Home » Area: \( w(2w + 4) = 104 \) - Silent Sales Machine

Area: \( w(2w + 4) = 104 \) - Silent Sales Machine

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 From (1): $w_2 = -1 - 2w_3$.

📌 From (2): $w_1 = 3w_3 - 4$.

📌 Substitute into (3):

📌 -2(3w_3 - 4) - 3(-1 - 2w_3) = 2 \

📌 -6w_3 + 8 + 3 + 6w_3 = 2 \Rightarrow 11 = 2

📌 Contradiction. Hence, no such vector $\mathbf{w}$ exists.

📌 oxed{ ext{No solution exists}}

📌 Question: A museum curator is restoring a triangular panel from a historical instrument, where the triangle has vertices at $A = (1, 3, -2)$, $B = (4, 1, 1)$, and $C = (2, -1, 3)$. Find the point $P$ on the line through $A$ and $B$ that is closest to point $C$.

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