申論題

2. Below is the figure of a wall and a door. Reference frame A is fixed to the wall (with the 3 mutually perpendicular directions â₁, â₂, and â₃). Similarly, reference frame B is fixed to the door. The door can be opened, and consequently the angle θ is a function of time. The height of the door is h, and the width is λ (both of them are constant scalars). Also, note that time derivative of θ is usually written as θ'

2.2. (3%) Another vector r is also shown in the figure. Use the addition rule of vectors, it is clear that. Please calculate . That is, express this vector in A frame, and then differentiate each component with respect to the angle θ.