Any vector of length 1 is called a [i]unit vector[/i]. There are three special unit vectors: the [i]standard unit vectors[/i]. These are [math]\mathbf{i}=\left\langle1,0,0\right\rangle[/math], [math]\mathbf{j}=\left\langle0,1,0\right\rangle[/math], and [math]\mathbf{k}=\left\langle0,0,1\right\rangle[/math].[br][br]Any vector can be written as a linear combination of the standard unit vectors. Use this interactive figure to explore how to write vectors as a linear combination of [math]\mathbf{i}[/math], [math]\mathbf{j}[/math], and [math]\mathbf{k}[/math]. Change the coefficients of [math]\mathbf{i}[/math], [math]\mathbf{j}[/math], and [math]\mathbf{k}[/math] in the window on the right and observe how the vector changes in the window on the left.[br]

[i]Developed for use with Thomas' Calculus, published by Pearson.[/i]