[color=#9900ff][b][size=150][center]Key Point[/center][/size][/b][/color][size=150]In two dimensions, the [b][color=#980000]unit vectors[/color][/b] in the directions of the two coordinate axes are written as[size=100] [math]\vec{i}[/math] and [math]\vec{j}[/math].[/size][br]If a point P has coordinates (x, y) then the [color=#980000][b]position vector[/b][/color] [math]\vec{\text{OP}}[/math] may be written as a l[u]inear combination of unit vectors: [/u][math]\vec{\text{OP}}=x\vec{i}+y\vec{j}[/math][br]or equivalently as a column vector [math]\vec{OP}=\binom{x}{y}[/math].[br]x and y are [u][color=#0000ff]scalars [/color][/u](real numbers) and they represent the [b][color=#0000ff]coordinates[/color][/b] of the point P.[br]The expression [math]x\vec{i}+y\vec{j}[/math] is a [color=#0000ff][b]vector[/b][/color].[br][br]Given an initial point of [b](0,0)[/b] and terminal point [b](a,b)[/b], a vector may be represented as [color=#0000ff][b](a,b)[/b][/color].[/size]