Displacement is just the vector pointing from where one starts to where one ends. You can even represent this on a one-dimensional line.
Imagine having a line with a point labeled "0," and then evenly spaced tick marks labeled 1, 2, 3, and so on, leading away in one direction (often to the right, for a horizontal line) and others labeled -1, -2, -3, and so on, in the other direction (left).
Suppose these tick marks represented "meters," and you wanted to represent yourself moving from 0 to 3 meters to the right. You begin at a position of 0 meters, and move to a position of 3 meters to the right. To represent this on your line, draw an arrow from the 0 tick mark pointing to the 3 tick mark. This arrow points from where you start to where you finish, and therefore represents your displacement. In this case, it would be a positive displacement, because it points in your positive direction.
Now, suppose you want to represent walking from the 0 position to -3 meters. You draw an arrow starting at 0, and ending at the -3 tick mark. This arrow has the same length as the other, but points in the opposite direction. This one would indicate a displacement of -3 m.
Both of the arrows you have drawn have the same length, which represents their magnitude, because, in both cases, you moved a distance of 3 meters. But, in the first case, you moved in the positive direction, and so had a positive displacement. In the second case, you moved in the negative direction and had a negative displacement.
Displacement is a vector because it indicates both magnitude (amount) AND direction. A negative vector just indicates the direction was negative, and a positive vector indicates the direction was positive.
In general, you can calculate displacement by:
displacement = (final position - initial position)
In the first case, the initial position was 0 and the final position was 3, so the displacement was 3-0 = 3 meters. In the second case, the initial position was 0 and the final position was -3, so the displacement was -3-0 = -3 meters. This is the mathematical way to get the sign for displacement.
I hope this helps! Just let me know if you have any more questions about this.
