The standard unit vectors
A unit vector is a vector whose magnitude (or length) is one. The standard unit vectors are the special unit vectors that are parallel to the coordinate axes, pointing toward positive values of the coordinate.
Two dimensions
The standard unit vectors in two dimensions. The standard unit vectors in two dimensions, $\vc{i}$ (green) and $\vc{j}$ (blue), are length one vectors that point parallel to the $x$-axis and $y$-axis, respectively. Moving them with the mouse doesn't change the vectors, as they always point toward the positive direction of their respective axis.
Three dimensions
Applet loading
The standard unit vectors in three dimensions. The standard unit vectors in three dimensions, $\vc{i}$ (green), $\vc{j}$ (blue), and $\vc{k}$ (red) are length one vectors that point parallel to the $x$-axis, $y$-axis, and $z$-axis respectively. Moving them with the mouse doesn't change the vectors, as they always point toward the positive direction of their respective axis.