Any vector can be scaled longer or shorter by multiplying by a scalar. Multiplying a vector by a scalar maintains the direction of the vector but changes the magnitude. [br][br]We already have unit vectors (with magnitude 1) directed along the x-axis and y-axis, these are [math]\hat{i}[/math] and [math]\hat{j}[/math], respectively.[br][br]We often want a [b]unit vector directed in the same direction as a given vector[/b].[br][br][list][/list]In the interactive graph, adjust the endpoint of [math]\vec{v}[/math] and note its components and the magnitude are given. [br][br]The vector labeled [math]\hat{u}[/math] is the unit vector in the same direction as [math]\vec{v}[/math] is calculated as [math]\frac{\vec{v}}{|\vec{v}|}[/math]. [br]Verify the components of the unit vector in the same direction as [math]\vec{v}[/math] for multiple vectors.