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Home » R \cos\alpha = 1, \quad R \sin\alpha = \sqrt3 - Dachbleche24

R \cos\alpha = 1, \quad R \sin\alpha = \sqrt3 - Dachbleche24

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 angle$, find the vector $\mathbf{w}$ such that $\mathbf{w} imes \mathbf{u} = \mathbf{v}$.

📌 Solution: Let $\mathbf{w} = \langle w_1, w_2, w_3

📌 angle$. The cross product $\mathbf{w} imes \mathbf{u} = \mathbf{v}$ can be written as:

📌 egin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \ w_1 & w_2 & w_3 \ 3 & -2 & 1 \end{vmatrix} = \langle -1, 4, 2

📌 Compute the cross product:

📌 \mathbf{w} imes \mathbf{u} = \langle w_2(1) - w_3(-2), w_3(3) - w_1(1), w_1(-2) - w_2(3)

📌 angle = \langle w_2 + 2w_3, 3w_3 - w_1, -2w_1 - 3w_2

📌 Set equal to $\mathbf{v} = \langle -1, 4, 2

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