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Home » From Princess to Khaleesi: Daenerys’ Legendary Transformation You Won’t Believe! - AssociationVoting

From Princess to Khaleesi: Daenerys’ Legendary Transformation You Won’t Believe! - AssociationVoting

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 Solution: Use the Pythagorean theorem since $\overrightarrow{OA}$ and $\overrightarrow{OB}$ are perpendicular. Compute $\|\overrightarrow{OC}\|^2 = (2\|\overrightarrow{OA}\|)^2 + (\|\overrightarrow{OB}\|)^2 = 4(25) + 144 = 100 + 144 = 244$. Thus, $\|\overrightarrow{OC}\| = \sqrt{244} = 2\sqrt{61}$. Final answer: $\boxed{2\sqrt{61}}$.

📌 Question: There exist constants $m$ and $n$ such that $\overrightarrow{OC} = m\overrightarrow{OA} + n\overrightarrow{OB}$, where $\overrightarrow{OA} = \begin{pmatrix} 1 \\ 2 \end{pmatrix}$, $\overrightarrow{OB} = \begin{pmatrix} -1 \\ 3 \end{pmatrix}$, and $\overrightarrow{OC} = \begin{pmatrix} 4 \\ 5 \end{pmatrix}$. Enter the ordered pair $(m, n)$.

📌 Solution: Set up the system:

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