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Home » Art from the Sea That Will Make You Dive Deeper into Nature’s Magic! - Anadea

Art from the Sea That Will Make You Dive Deeper into Nature’s Magic! - Anadea

📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 ec{OA} \cdot ec{OB} = (-1 + \sqrt{7})(-1 - \sqrt{7}) + (1 + \sqrt{7})(1 - \sqrt{7})

📌 = [(-1)^2 - (\sqrt{7})^2] + [1 - (\sqrt{7})^2] = (1 - 7) + (1 - 7) = -6 -6 = -12

📌 Magnitudes:

📌 |ec{OA}| = \sqrt{(-1 + \sqrt{7})^2 + (1 + \sqrt{7})^2} = \sqrt{(1 - 2\sqrt{7} + 7) + (1 + 2\sqrt{7} + 7)} = \sqrt{16 + 8} = \sqrt{24} = 2\sqrt{6}

📌 |ec{OB}| = \sqrt{(-1 - \sqrt{7})^2 + (1 - \sqrt{7})^2} = \sqrt{(1 + 2\sqrt{7} + 7) + (1 - 2\sqrt{7} + 7)} = \sqrt{16 + 8} = \sqrt{24} = 2\sqrt{6}

📌 \cos heta = rac{-12}{(2\sqrt{6})(2\sqrt{6})} = rac{-12}{24} = -rac{1}{2} \Rightarrow heta = rac{2\pi}{3}

📌 The area of the circular sector is:

📌 A_{ ext{sector}} = rac{1}{2} r^2 heta = rac{1}{2} \cdot 16 \cdot rac{2\pi}{3} = rac{16\pi}{3}

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