Solution: To find the maximum possible value of \(\mathbf{u} \cdot \mathbf{w}\), we start by using the Cauchy-Schwarz inequality: \(|\mathbf{u} \cdot \mathbf{w}| \leq \|\mathbf{u}\| \|\mathbf{w}\| = 8\). This gives the bound \( -8 \leq \mathbf{u} \cdot \mathbf{w} \leq 8\). However, we must incorporate the given dot products \(\mathbf{u} \cdot \mathbf{v} = 1\) and \(\mathbf{v} \cdot \mathbf{w} = 6\).

Sun, 03 May 2026 23:32:36 +0000

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