For a unit vector [tex]\vec y[/tex], we have
[tex]\vec y\cdot\vec y=\|\vec y\|^2=1^2=1[/tex]
Recall that
[tex]\vec x\cdot\vec y=\|\vec x\|\|\vec y\|cos\theta[/tex]
where [tex]\theta[/tex] is the angle between the vectors [tex]\vec x[/tex] and [tex]\vec y[/tex].
Taking these facts together, we have
[tex]\dfrac{\vec x\cdot\vec y}{\vec y\cdot\vec y}\vec y=\|\vec x\|\cos\theta\,\vec y[/tex]
