The direction of its displacement wil be
c.northeast
In fact, the dog walks north for 10 meters and east for another 10 meters. The path of the dog can be represented with two vectors, A pointing north (of magnitude 10 meters) and B pointing east (of magnitude 10 meters). The direction of the resultant vector (due to east) will be given by
[tex] tan \theta =\frac{A}{B}=\frac{10}{10}=1 [/tex]
[tex] \theta=tan^{-1} (1)=45^{\circ} [/tex]
and the direction will be north-east.
