"Maybe insert an equation style definition of th..."

This fact also gives us a way to ignore the magnitude, and just focus on the direction of a vector\. We can scale a vector by the inverse of its magnitude to get a vector with magnitude 1 with the same direction, called $~${\\bf \\hat v}$~$\. $$~$|\\mathbf{\\hat v}| \= \\left|\\frac{\\mathbf{v}}{|\\mathbf{v}|}\\right| \= \\left|\\frac{1}{|\\mathbf{v}|}\\right||\\mathbf{v}| \= \\frac{|\\mathbf{v}|}{|\\mathbf{v}|}\=1$~$$

Maybe insert an equation style definition of the unit vector here, before showing that it has magnitude 1.

$~$\hat{\mathbf v} = \frac{1}{| \mathbf v |}\mathbf v = \frac{\mathbf v}{| \mathbf v |}$~$.