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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 $\boxed{\dfrac{1}{2}}$. 📰 Chitlins 2502392 📰 Never Guess Again This Shower Valve Secret Will Transform Your Bath 193632 📰 You Wont Believe Whats Included In This All Inclusive Bermuda Escape 8483577 📰 You Wont Believe These Skeletons Taking Over Memesreload Now 6937545 📰 Wizards Beyond Waverly Place Episodes 1079242 📰 The Shocking Truth About Tufesas Hidden Method No One Talks About 6947792 📰 Unlock Faster Collaboration With Our Pro Raci Template Excel 1750393 📰 Paris Creperie 7665139 📰 Chattanooga To Nashville 8356842 📰 2025 Memorial Day 4065773 📰 Jonathan Bailey Jurassic World 3890111 📰 Lookout Tower 9896704 📰 Park Avenue Apartments 7885050 📰 Naked Attraction Tv Show 2680834 📰 But If The Surface Is Curved Then Rays Not Parallel 7427315