The coordinates of a particle with respect to origin in a given reference frame is (1, 1, 1) meters. If a force of $$\overrightarrow{F} = \hat{i} - \hat{j} + \hat{k}$$ acts on the particle, then the magnitude of torque (with respect to origin) in z-direction is_________.

We need to find the magnitude of torque in the z-direction when a force $$\vec{F} = \hat{i} - \hat{j} + \hat{k}$$ acts on a particle at position $$\vec{r} = \hat{i} + \hat{j} + \hat{k}$$ (coordinates (1, 1, 1) m).

Recall that torque is given by $$\vec{\tau} = \vec{r} \times \vec{F}$$.

Substituting the given vectors into the determinant,
$$\vec{\tau} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 1 & 1 & 1 \\ 1 & -1 & 1 \end{vmatrix}$$
$$= \hat{i}(1 \cdot 1 - 1 \cdot (-1)) - \hat{j}(1 \cdot 1 - 1 \cdot 1) + \hat{k}(1 \cdot (-1) - 1 \cdot 1)$$
$$= \hat{i}(1 + 1) - \hat{j}(1 - 1) + \hat{k}(-1 - 1)$$
$$= 2\hat{i} - 0\hat{j} - 2\hat{k}$$

The z-component of torque is $$\tau_z = -2$$, so the magnitude of torque in the z-direction is $$|\tau_z| = 2$$.

The answer is 2.