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📅 May 11, 2026 👤 scraface

May 11, 2026

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\vec{w} = \begin{pmatrix} 2 \cdot 3 \\ 2 \cdot (-1) \\ 2 \cdot 2 \end{...
Subtract the vectors component-wise:
\vec{w} = \begin{pmatrix} 6 - (-6) \\ -2 - 12 \\ 4 - 3 \end{pmatrix} =...
Thus, the vector $\vec{w}$ is:
\boxed{\begin{pmatrix} 12 \\ -14 \\ 1 \end{pmatrix}}
Question: A hydrologist models the flow of groundwater in a 3D aquifer...
Let the point on the line be $\vec{r}(t) = \begin{pmatrix} 1 + 2t \\ t...
Let $P = (3, -1, 2)$. The vector from the point on the line to $P$ is:
\vec{d}(t) = \vec{P} - \vec{r}(t) = \begin{pmatrix} 3 - (1 + 2t) \\ -1...
To find the closest point, minimize the magnitude of $\vec{d}(t)$, or...

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