Does displacement depend on direction and what is it's formula?

'Distance' is how far you walk on your afternoon walk, while you cut across the park, go two blocks out of your way to visit a friend, and cross the street several times in both directions to avoid some big-looking dogs. Every step counts for distance.  Distance only has a size but no direction, because the direction could change a hundred times during the trip. And from the time you leave home until you return home, the distance could be 5 miles or more.   

'Displacement' is very different.  Displacement is just the straight-line distance between the starting point and the end point, regardless of the route that was
followed between them.  It has a size ... the distance between them, and it also has a direction ... the direction from start to finish.  And if you start out from home and return home, then your displacement for that trip is zero, because there's no straight-line distance from the starting point to the end point.