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Compute $ \mathbfv \times \mathbfa $: - Get link 4share

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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\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...
\|\vec{d}(t)\|^2 = (2 - 2t)^2 + (-1 - t)^2 + (5 + t)^2
Add them up:
\|\vec{d}(t)\|^2 = (4 - 8t + 4t^2) + (1 + 2t + t^2) + (25 + 10t + t^2)...
Take derivative and set to 0:

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