A girl walks 2.6km North then 4.0 km East and finally 3.1 km N of E at a 45 degree angle.
In the vector representation, her displacements can be represented as in line a) of the attached figure.
Two of the vectors are at perpendicular direction and the third one is disposed t an angle. Addition of vectors at right angles is easy, but not so for a vector at an angle. It can be resolved into two perpendicular components as in line b) of the figure.
When the orders of execution of these vectors are rearranged, the addition step becomes even simplified as shown in line c) of the figure.
The resultant can be found out using the law of triangles:
Therefore, overall displacement of the girl is 7.83 km.