# Question #a1bdc

Dec 8, 2015

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 $\left(x , y\right) = \left(2 , 3\right)$ and ends at the point whose rectangular coordinates are $\left(x , y\right) = \left(- 4 , 7\right)$, then the displacement vector can be drawn as an arrow staring at $\left(2 , 3\right)$ and ending at $\left(- 4 , 7\right)$. 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 $\vec{v} = - 6 \hat{i} + 4 \hat{j}$, 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.