The Cartesian coordinates of a point $P$ in a right-handed coordinate system are $(1, 1, 1)$. The transformed coordinates of $P$ due to a $45^{\circ}$ clockwise rotation of the coordinates system about the positive $x$-axis are
- $\left ( 1, 0, \sqrt{2} \right )$
- $\left ( 1, 0, -\sqrt{2} \right )$
- $\left ( -1, 0, \sqrt{2} \right )$
- $\left ( -1, 0, -\sqrt{2} \right )$