The steering wheel and gearshift lever of an automobile are shown. Points A, C, and B li...

The steering wheel and gearshift lever of an automobile are shown. Points A, C, and B lie on the axis of the steering column, where point A is at the origin of the coordinate system, point B has the coordinates B(120, 0, -50) mm, and point C is 60 mm from point A. The gearshift lever from C to D has 240 mm length and the direction angles given below.

(a) Two of the direction angles for the position vector from point C to D are θ_y = 45^o and θ_z = 70^o. Knowing that this position vector has a negative x component, determine θ_x.

(b) Determine the unit vector that is perpendicular to directions AB and CD such that this vector has a positive z component.

(c) If the force applied to the gear shift lever is determine the component of namely P_r, in the direction of