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📰 Solution: The dot product of two unit vectors is $\mathbf{u} \cdot \mathbf{v} = \cos\theta$. Given $\cos\theta = \frac{\sqrt{3}}{2}$, the angle $\theta$ satisfies $\theta = \arccos\left(\frac{\sqrt{3}}{2}\right)$. This corresponds to $\theta = 30^\circ$ or $\frac{\pi}{6}$ radians. However, since cosine is positive in both the first and fourth quadrants, but angles between vectors are typically taken in $[0, \pi]$, the solution is $\boxed{\dfrac{\pi}{6}}$. 📰 Question: A biochemistry technician measures the angle between two molecular bonds modeled as vectors $\mathbf{a} = \begin{pmatrix} 1 \\ 0 \\ 1 \end{pmatrix}$ and $\mathbf{b} = \begin{pmatrix} 0 \\ 1 \\ 1 \end{pmatrix}$. Compute $\cos\theta$ where $\theta$ is the angle between them. 📰 Solution: The cosine of the angle between vectors $\mathbf{a}$ and $\mathbf{b}$ is given by $\cos\theta = \frac{\mathbf{a} \cdot \mathbf{b}}{\|\mathbf{a}\| \|\mathbf{b}\|}$. Compute the dot product: $\mathbf{a} \cdot \mathbf{b} = (1)(0) + (0)(1) + (1)(1) = 1$. The magnitudes are $\|\mathbf{a}\| = \sqrt{1^2 + 0^2 + 1^2} = \sqrt{2}$ and $\|\mathbf{b}\| = \sqrt{0^2 + 1^2 + 1^2} = \sqrt{2}$. Thus, $\cos\theta = \frac{1}{\sqrt{2} \cdot \sqrt{2}} = \frac{1}{2}$. The final answer is $\boxed{\dfrac{1}{2}}$. 📰 Tv Backlight 7240195 📰 Buscas La Alternativa Perfecta Esta Es La Que Te Har Cambiar Tu Forma De Trabajar Deportivamente 2152427 📰 Yellow Colour Yellow 1076537 📰 From Blank Paper To Gripping Art See How Drawn In Pencil Transforms Every Stroke 8042239 📰 Unlock Hidden Excel Power Auto Calculate In Word Tableseasy Steps Inside 7773645 📰 Gg Smart Lock 5504027 📰 Barbie Ferreira Weight Loss 6613705 📰 Khwhi Exposed The Truth About Kwh Youve Been Manipulated About 8539990 📰 Discover How Recruiting Stocks Can Transform Your Investment Portfolio Overnight 8881431 📰 Devastating Crash On I 75 Todayinjuries Reported Emergency Services Overwhelmed 951828 📰 This Is Why Gotham Fears The Justice League Gods Monsterswatch Now 3708572 📰 Define Serf 2583550 📰 Verizon Fioz Login 4573487 📰 Game That Challenges Your Reflexes Like Never Beforecheck Empowered Speed 9682834 📰 Youll Be Shocked When Hydrangeas Bloom The Ultimate Seasonal Guide 1480945