What is the total displacement of an ant that walks 2 meters west, 3 meters south, 4 meters east, and 1 meter north?

(2m west) + (3m south) + (4m east) + (1m north) =

[ (2m west)+(4m east) ] + [ (3m south)+(1m north) ] =

[ (-2m east)+(4m east) ] + [ (3m south)-(1m south) ] =

(2m east) + (2m south)

Now, so far, we have the orthogonal (perpendicular) components of the displacement ... the North/South component and the East/West component.

To combine these, it's time for Pythagoras:

Displacement = √[ (2m)² + (2m)² ]

Displacement = √ (4m² + 4m²)

Diplacement = √8m²  

Displacement =  2.83 meters Southeast

no. dot product   =0 when vecs at right angles