![]()
**Shocking Truth: How
🔗 Related Articles You Might Like:
📰 \( U(4) = \frac{10,000}{2.2177} \approx 4,509.9 \)
📰 #### 4,509.9Question: In a quantum communication network, consider vectors \(\mathbf{u}, \mathbf{v},\) and \(\mathbf{w}\) in \(\mathbb{R}^3\) with \(\|\mathbf{u}\| = 2\), \(\|\mathbf{v}\| = 3\), and \(\|\mathbf{w}\| = 4\). If \(\mathbf{u} \cdot \mathbf{v} = 1\) and \(\mathbf{v} \cdot \mathbf{w} = 6\), determine the maximum possible value of \(\mathbf{u} \cdot \mathbf{w}\).
📰 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 \(\mathbf{v} \cdot \mathbf{w} = 6\).
