Question

Question #a1bdc

Answer 1

A displacement vector is just a way of representing a change in position. It's an arrow that points from a starting location to an ending location.

Explanation:

For example, if a person is walking on a flat surface that we have (mentally) imposed a rectangular coordinate system on, and if the person starts at the point whose rectangular coordinates are `(x,y)=(2,3)` and ends at the point whose rectangular coordinates are `(x,y)=(-4,7)`, then the displacement vector can be drawn as an arrow staring at `(2,3)` and ending at `(-4,7)`. The time elapsed is irrelevant for determining the displacement vector (but not irrelevant for determining the average velocity vector).

The so-called "components" of the displacement vector are the differences of the corresponding coordinates: `-4-2=-6` and `7-3=4` (the displacement is 6 units to the left and 4 units upward in the plane the person is walking on). The vector is then often written algebraically as `vec(v)=-6hat(i)+4hat(j)`, where `hat(i)` is a "unit" vector (length one) pointing directly to the right (in the positive `x`-direction) and `hat(j)` is a unit vector pointing directly upward (in the positive `y`-direction) in the plane the person is walking on.

The person does not have to walk in a straight line, but the displacement vector itself is straight.