4. An object located at the origin in a three-dimensional coordinate system is held in equilibrium by four forces. One has magnitude 7 lb and points in the direction of the positive $x$-axis, so it is represented by the vector $7\hat{i}$. The second has magnitude 24 lb and points in the direction of the positive $y$-axis. The third has magnitude 25 lb and points in the direction of the negative $z$-axis.
(a) (8 points) Use the fact that the four forces are in equilibrium (that is, their sum is 0) to find the fourth force. Express your answer in terms of the unit vectors $\hat{i}$, $\hat{j}$, and $\hat{k}$.
(b) (5 points) What is the magnitude of the forth force?