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Home » Durchschnittsgeschwindigkeit**: \(350 \div 4 = 87.5 \, \textkm/h\) - Network4

Durchschnittsgeschwindigkeit**: \(350 \div 4 = 87.5 \, \textkm/h\) - Network4

📅 May 19, 2026 👤 scraface

May 19, 2026

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📌 \mathbf{u} = \frac{1}{\|\mathbf{g}\|} \mathbf{g} = \frac{1}{25} \begin{pmatrix} 7 \\ 24 \end{pmatrix} = \begin{pmatrix} \frac{7}{25} \\ \frac{24}{25} \end{pmatrix}

📌 Thus, the normalized vector is:

📌 \boxed{\begin{pmatrix} \frac{7}{25} \\ \frac{24}{25} \end{pmatrix}}

📌 A hydrologist models contaminant spread using vectors $\mathbf{p} = \begin{pmatrix} 4 \\ -1 \\ 3 \end{pmatrix}$ and $\mathbf{q} = \begin{pmatrix} 2 \\ 0 \\ -1 \end{pmatrix}$. Find the projection of $\mathbf{p}$ onto $\mathbf{q}$.

📌 The projection of $\mathbf{p}$ onto $\mathbf{q}$ is given by:

📌 \text{proj}_{\mathbf{q}} \mathbf{p} = \frac{\mathbf{p} \cdot \mathbf{q}}{\|\mathbf{q}\|^2} \mathbf{q}

📌 First, compute the dot product:

📌 \mathbf{p} \cdot \mathbf{q} = 4(2) + (-1)(0) + 3(-1) = 8 + 0 - 3 = 5

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