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Home » BIGGEST MATTRESS EVER? Discover the Largest Bed Size That Wizards Swear By! - jntua results

BIGGEST MATTRESS EVER? Discover the Largest Bed Size That Wizards Swear By! - jntua results

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 \boxed{\begin{pmatrix} 2 \\ 0 \\ -1 \end{pmatrix}}

📌 An astrophysics researcher analyzes stellar motion with vectors $\mathbf{r} = \begin{pmatrix} 1 \\ 2 \\ -1 \end{pmatrix}$ and $\mathbf{s} = \begin{pmatrix} -2 \\ 1 \\ 4 \end{pmatrix}$. Find the area of the parallelogram spanned by $\mathbf{r}$ and $\mathbf{s}$.

📌 The area is the magnitude of the cross product $\mathbf{r} \times \mathbf{s}$:

📌 \mathbf{r} \times \mathbf{s} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 1 & 2 & -1 \\ -2 & 1 & 4 \end{vmatrix}

📌 = \mathbf{i}(2 \cdot 4 - (-1) \cdot 1) - \mathbf{j}(1 \cdot 4 - (-1)(-2)) + \mathbf{k}(1 \cdot 1 - 2 \cdot (-2))

📌 = \mathbf{i}(8 + 1) - \mathbf{j}(4 - 2) + \mathbf{k}(1 + 4)

📌 = 9\mathbf{i} - 2\mathbf{j} + 5\mathbf{k} = \begin{pmatrix} 9 \\ -2 \\ 5 \end{pmatrix}

📌 Now compute its magnitude:

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Define $ g(u) = 3u^2 - 4u^4 $, $ u \in [-1, 1] $.
g'(u) = 6u - 16u^3 = 2u(3 - 8u^2)
Set $ g'(u) = 0 $: $ u = 0 $ or $ 3 - 8u^2 = 0 \Rightarrow u^2 = rac{...
Evaluate $ g(u) $:
At $ u = 0 $: $ g = 0 $
At $ u = \pm rac{\sqrt{6}}{4} $:
g = 3\left(rac{6}{16}
ight) - 4\left(rac{36}{256}
ight) = rac{18}{16} - rac{144}{256} = rac{9}{8} - rac{9}{16} = ra...
So maximum of $ \sin 3x \sin x $ is $ rac{9}{16} $, thus minimum of $...

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