Question

After an airplane takes off, it travels 1 km north, and then 2 km east. How far and in what direction is it from the take-off point?

Answer 1

The magnitude of displacement

$$d=\sqrt{1^2+2^2}=2.24\:\rm km$$

The direction

$$\theta=\tan^{-1}\frac{1}{2}=27^\circ\quad \rm(N\; of\; E)$$