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Home » 0.15x + 0.40y = 0.25 imes 10 - Londonproperty

0.15x + 0.40y = 0.25 imes 10 - Londonproperty

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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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:
\frac{d}{dt}(6t^2 + 4t + 30) = 12t + 4 = 0 \Rightarrow t = -\frac{1}{3...
Substitute $t = -\frac{1}{3}$ into $\vec{r}(t)$:
\vec{r}\left(-\frac{1}{3}\right) = \begin{pmatrix} 1 + 2(-\frac{1}{3})...
Thus, the closest point is:
\boxed{\begin{pmatrix} \frac{1}{3} \\ -\frac{1}{3} \\ -\frac{8}{3} \en...

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