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 θy = 50o and θz = 60o. Knowing that this position vector has a negative x component, determine θx.
(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 gearshift lever is namely Pr, in the direction of .
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