For any scalar [tex]t>0[/tex], [tex]t\vec a[/tex] is a vector pointing in the same direction as [tex]a[/tex].
To force this vector to have the same length as another vector [tex]\vec b[/tex], first normalize [tex]t\vec a[/tex] by dividing it by its norm,
[tex]\dfrac{t\vec a}{\|t\vec a\|}=\dfrac{t\vec a}{t\|\vec a\|}=\dfrac{\vec a}{\|\vec a\|}[/tex]
then multiply this vector by the norm of [tex]\vec b[/tex], so that
[tex]\vec c=\dfrac{\|\vec b\|}{\|\vec a\|}\vec a[/tex]
To confirm that [tex]\vec c[/tex] has the same length as [tex]\vec b[/tex]:
[tex]\|\vec c\|=\left\|\dfrac{\|\vec b\|}{\|\vec a\|}\vec a\right\|=\dfrac{\|\vec b\|}{\|\vec a\|}\|\vec a\|=\|\vec b\|[/tex]
