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5 gallon water bottle jug - Coaching Toolbox

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 \mathbf{r}(t) = \mathbf{A} + t(\mathbf{B} - \mathbf{A}) = \langle 1, 3, -2

📌 angle + t\langle 3, -2, 3

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

📌 Let $P = \mathbf{r}(t)$. The vector $\overrightarrow{CP} = \mathbf{r}(t) - \mathbf{C} = \langle 1 + 3t - 2, 3 - 2t + 1, -2 + 3t - 3

📌 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) \

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