Vector in Two Dimensions (2-D)

Restricting to a single plane, the set of all combinations $x\bar a+y\bar b$ (for real $x,y$) of two

non-collinear vectors $\bar a,\bar b$ sweeps out the entire plane; $\bar a,\bar b$ are then called the

generators of that plane, and $\{\bar a,\bar b\}$ its basis. The most useful basis is the pair of

standard unit vectors: taking $M=(1,0)$ on the X-axis and $N=(0,1)$ on the Y-axis, define

$\hat\imath=\overrightarrow{OM}$ and $\hat\jmath=\overrightarrow{ON}$. Then any vector $\overrightarrow{OP}$

to a point $P=(x,y)$ is $x\hat\imath+y\hat\jmath$ -- for instance, the point $P=(3,4)$ gives …