The steering column of the rack-and-pinion steering mechanism lies in the xz-plane. The tube AB of the steering gear is attached to the automobile chassis at A and B. When the steering wheel is turned, the assembly is subjected to the four couples shown: the 3-N·m couple applied by the driver to the steering wheel, two 1.8-N · m couples (one at each wheel), and the couple formed by the two forces of magnitude F acting at A and B. If the resultant couple acting on the steering mechanism is zero, determine F and the angle θ (the magnitude and direction of the bearing reactions).
