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📅 May 19, 2026 👤 scraface

May 19, 2026

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📌 angle = \langle -1 + 3t, 4 - 2t, -5 + 3t

📌 To minimize the distance, minimize $\|\overrightarrow{CP}\|^2$:

📌 D^2 = (-1 + 3t)^2 + (4 - 2t)^2 + (-5 + 3t)^2

📌 = (1 - 6t + 9t^2) + (16 - 16t + 4t^2) + (25 - 30t + 9t^2) \

📌 = 42 - 52t + 22t^2

📌 Take derivative and set to zero:

📌 rac{d}{dt}(42 - 52t + 22t^2) = -52 + 44t = 0 \Rightarrow t = rac{13}{11}

📌 Substitute $t = rac{13}{11}$ into $\mathbf{r}(t)$:

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