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Home » The speed of the train is \( \frac{120 \text km}{1.5 \text hours} = 80 \text km/h \). - Dyverse

The speed of the train is \( \frac{120 \text km}{1.5 \text hours} = 80 \text km/h \). - Dyverse

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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Solution: To find a vector orthogonal to both, compute their cross pro...
\begin{pmatrix} 1 \\ -2 \\ 3 \end{pmatrix} \times \begin{pmatrix} 4 \\...
= \mathbf{i}((-2)(-1) - (3)(0)) - \mathbf{j}((1)(-1) - (3)(4)) + \math...
= \mathbf{i}(2) - \mathbf{j}(-1 - 12) + \mathbf{k}(0 + 8) = 2\mathbf{i...
Thus, the vector is $\boxed{\begin{pmatrix} 2 \\ 13 \\ 8 \end{pmatrix}...
Question:** A linguist modeling word embeddings in 3D space defines tw...
Solution:** The dot product of two unit vectors is given by $\mathbf{u...
|\mathbf{u} \cdot \mathbf{v}| = |\cos 60^\circ| = \left|\frac{1}{2}\ri...
Question:** A cloud computing system routes data along vectors in $\ma...
Solution:** Let $\mathbf{v} = \begin{pmatrix} x \\ y \\ z \end{pmatrix...

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