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avon old farms hotel - IQnection

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Therefore, the angle between $ \vec{v} $ and $ \vec{w} $ is $ \frac{2\pi}{7} $.

📌 \boxed{\frac{2\pi}{7}}

📌 Question: A pharmacologist is modeling the interaction of two molecules as vectors in 3D space. If molecule A is represented by $ \vec{a} = (1, 2, 3) $ and molecule B by $ \vec{b} = (4, 5, 6) $, find the area of the parallelogram formed by these vectors.

📌 Solution: The area of the parallelogram formed by vectors $ \vec{a} $ and $ \vec{b} $ is the magnitude of their cross product:

📌 \vec{a} \times \vec{b} =

📌 & 5 & 6 \\

📌 = \mathbf{i}(2 \cdot 6 - 3 \cdot 5) - \mathbf{j}(1 \cdot 6 - 3 \cdot 4) + \mathbf{k}(1 \cdot 5 - 2 \cdot 4)

📌 = \mathbf{i}(12 - 15) - \mathbf{j}(6 - 12) + \mathbf{k}(5 - 8)

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