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📰 Solution: The magnitude of the cross product is $\|\mathbf{p} \times \mathbf{q}\| = \|\mathbf{p}\| \|\mathbf{q}\| \sin\theta$. Since $\mathbf{p}$ and $\mathbf{q}$ are unit vectors, $\|\mathbf{p} \times \mathbf{q}\| = \sin\theta = \frac{1}{2}$. Thus, $\theta = \arcsin\left(\frac{1}{2}\right)$, which gives $\theta = \frac{\pi}{6}$ or $\frac{5\pi}{6}$. However, the angle between vectors is taken as the acute angle, so $\theta = \boxed{\dfrac{\pi}{6}}$. 📰 Question: A biochemistry technician studies protein folding angles, modeling bonds as vectors $\mathbf{m} = \begin{pmatrix} x \\ 2 \end{pmatrix}$ and $\mathbf{n} = \begin{pmatrix} 1 \\ -1 \end{pmatrix}$. Find $x$ such that $\mathbf{m}$ and $\mathbf{n}$ are orthogonal. 📰 Solution: For vectors to be orthogonal, their dot product must be zero: $\mathbf{m} \cdot \mathbf{n} = x(1) + 2(-1) = x - 2 = 0$. Solving gives $x = 2$. The final answer is $\boxed{2}$. 📰 Oracle Developer Secrets Exposed Land The Dream Tech Job In 7 Steps 1464854 📰 Win 11 Upgrade Assistant 5680122 📰 These 5 Whisky Drink Brands Are Rocking The Bar Sceneyou Wont Believe How Bad They Taste 8900099 📰 Defaultdict Python 📰 What Is Scat 2285234 📰 Ethereum Macro Super Cycle Tom Lee 📰 Stop Trusting This Fluidwhat Hidden Secrets Lie Inside 9305022 📰 Nbc Tv Tonight 6982168 📰 Combinando Ambos Casos Las Soluciones Son 3717531 📰 Nc Test Admin 5432277 📰 Another Word For Transparency 7833159 📰 3 Guaranteed Income Annuity That Pays More Every Monthproven Formula Inside 4150717 📰 See Your Nose Transformation Before After Surgery Photos So Stunning 8322989 📰 Anthropic News 2605751 📰 Comedy Night Game 4345751