Find the torque of a force $F = 7\hat{i} + 3\hat{j} - 5\hat{k} ext{ N}$ acting on a particle whose

Question

Find the torque of a force $F = 7\hat{i} + 3\hat{j} - 5\hat{k}	ext{ N}$ acting on a particle whose position vector is $r = \hat{i} - \hat{j} + \hat{k}	ext{ m}$ about the origin.

Professor PC Thomas Classes · Answer

Torque $	au = r 	imes F$. Using the determinant method: $	au = \hat{i}((-1)(-5) - (1)(3)) - \hat{j}((1)(-5) - (1)(7)) + \hat{k}((1)(3) - (-1)(7)) = \hat{i}(5-3) - \hat{j}(-5-7) + \hat{k}(3+7) = 2\hat{i} + 12\hat{j} + 10\hat{k}	ext{ Nm}$.