A fluid particle moving in a general three-dimensional flow field may rotate about all three coordinate axes. Thus particle rotation is a vector quantity and, in general, \[ \vec{\omega} = \omega_x \hat{i} + \omega_y \hat{j} + \omega_z \hat{k} \] where \(\omega_x\) is the rotation about the \(x\) axis, \(\omega_y\) is the rotation about the \(y\) axis, and \(\omega_z\) is the rotation about the \(z\) axis. The positive sense of rotation is given by the right-hand rule