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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 $\boxed{2}$. 📰 Windows 2024 Fixed Windows For Old Pcs Youve Been Searching For 2615569 📰 Hipaa Law Secrets That No One Wants You To Miss Before Its Too Late Find Out Now 8771232 📰 Why 10M Users Swear By The Contact Manager Iphone Appdownload Now 6769010 📰 No Es Solo Un Ranchito Es El Sueo Hecho Realidad A Pocos Pasos De Tu Casa 6537953 📰 Ninacolas Dark Truth The Hidden Agony Behind The Smile 4422577 📰 How Many Seasons Game Of Thrones Are There 2291599 📰 Flex Payments The Future Of Payments You Wont Want To Skip 4803535 📰 Zoopla Secrets How To Find Your Perfect Home Faster Than Ever 671952 📰 Uche Ojeh 8059953 📰 Forest Lost To Logging 030 4800 030480014401440 Acres 181951 📰 Another Word For Resonates 6327455 📰 Tyx Stock Soared 300Stockmarkets Hot Surprise You Cant Miss 1176449 📰 Guaranteed Lifetime Income Annuity 5279783 📰 Banking Business Account 9434153 📰 Sam Edelman Mary Jane 4123413