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📅 May 4, 2026 👤 scraface

May 04, 2026

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🔥 Popular Posts

Question: A philosopher of science considers three unit vectors $ \mat...
Solution: Since $ \mathbf{a}, \mathbf{b}, \mathbf{c} $ are unit vector...
\|\mathbf{a} + \mathbf{b} + \mathbf{c}\|^2 = \|\mathbf{a}\|^2 + \|\mat...
= 3 + 2(\mathbf{a} \cdot \mathbf{b} + \mathbf{b} \cdot \mathbf{c} + \m...
Each dot product $ \leq 1 $, and maximum occurs when $ \mathbf{a} = \m...
\|\mathbf{a} + \mathbf{b} + \mathbf{c}\|^2 = 3 + 2(1 + 1 + 1) = 3 + 6...
\Rightarrow \|\mathbf{a} + \mathbf{b} + \mathbf{c}\| = 3
This is achievable when all vectors are equal.
Thus, the maximum value is $ \boxed{3} $.
Question: A regular tetrahedron has three of its vertices at $ (1,1,1)...

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