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Home » E) $ \frac\pi r^2c^2 $ - Imagemakers

E) $ \frac\pi r^2c^2 $ - Imagemakers

📅 April 30, 2026 👤 scraface

Apr 30, 2026

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📌 To find the unit vector $\mathbf{u}$, compute the magnitude of $\mathbf{g}$:

📌 \|\mathbf{g}\| = \sqrt{7^2 + 24^2} = \sqrt{49 + 576} = \sqrt{625} = 25

📌 The unit vector is:

📌 \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:

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