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Problem 504

A particle is at the origin of the \(\mathrm{x}, \mathrm{y}\) and \(\mathrm{z}\) axis in the standard coordinate system in \(\mathrm{R}^{3}\). The particle is subject to the following forces: \(\mathrm{F}_{1}\) : force of 5 units acting along \(0 \mathrm{x}\) \(\mathrm{F}_{2}\) : force of 3 units acting along \(z 0\) \(\mathrm{F}_{3}:\) force of 2 units acting along \(0 \mathrm{y}\) \(\mathrm{F}_{4}\) : force of $2 \sqrt{2}\( units acting towards 0 at an angle of \)\pi / 4\( to the \)\mathrm{x}$ and \(\mathrm{y}\) axes in the xy plane. Find the resultant force on the particle.

Expert verified

The resultant force on the particle has a magnitude of \( \sqrt{74} \) units and direction angles \(\alpha, \beta, \gamma\) with respect to the x, y, and z axes respectively, where \(\alpha = \cos^{-1} \left(\frac{7}{\sqrt{74}}\right), \beta = \cos^{-1} \left(\frac{4}{\sqrt{74}}\right)\), and \(\gamma = \cos^{-1} \left(\frac{3}{\sqrt{74}}\right)\).

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