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Geometry Level 2

Consider the force vector \(\textbf{F} = \langle1, 1 \frac{1}{2}\rangle\) . If the magnitude of the torque \(\tau = \overline{OP}\times\textbf{F}\) is equal to the area of the equilateral triangle formed by the origin, \(P\), and \((1, -1, 1)\), then determine the acute angle formed by \(\overline{OP}\) and \(\textbf{F}\). Give your answer in degrees.

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