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'

2.1. (4%) A vector g is fixed to the upper edge of the door. Thus, g = λˆb₂. Please express vector g in A frame. Hint: Use the following top view to express ˆb₂ in A frame. That is ˆb₂ = (  )â₁ + (. )â₂. Fill in the blanks.