Assume all vectors lie in a 3D subspace. Express \(\mathbf{u}\) and \(\mathbf{w}\) in terms of an orthonormal basis adapted to the constraints. Use geometric insight: the maximum \(\mathbf{u} \cdot \mathbf{w}\) occurs when \(\mathbf{u}\) and \(\mathbf{w}\) are aligned as much as possible, consistent with intermediate alignments to \(\mathbf{v}\).

Sat, 02 May 2026 20:02:32 +0000

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