A drone takes off from point A on level ground and follows this flight plan:
1. Ascends vertically 200 m.
2. Flies 1.0 km due east while maintaining its altitude.
3. Flies 600 m due north while simultaneously climbing a further 100 m.
4. Flies 800 m due west while descending 150 m.
Let the east, north and upward vertical directions be represented by the unit vectors i^,j^,k^ respectively. Answer the following:
a. (i) Write each of the four flight legs as a three-dimensional displacement vector xi^+yj^+zk^.
b. (ii) Determine the resultant displacement vector of the drone from point A after completing all four legs.
c. (iii) Calculate the magnitude of this resultant displacement. Also find the angle that the resultant makes with the horizontal plane, correct to one decimal place.
d. (iv) Compute the vertical distance the drone must change and the horizontal distance it must cover to return directly to point A along the shortest straight path.