Normalize [tex]\vec u[/tex] by dividing [tex]\vec u[/tex] by its magnitude:
[tex]\dfrac{\vec u}{\|\vec u\|}=\dfrac{(1,-2,4)}{\sqrt{1^2+(-2)^2+4^2}}=\dfrac{(1,-2,4)}{\sqrt{21}}[/tex]
Multiply by -1 to reverse its direction, and again by [tex]\sqrt3[/tex] to ensure this new vector has the magnitude we want. Notice that [tex]\sqrt{\dfrac3{21}}=\dfrac1{\sqrt7}[/tex].
[tex]-\sqrt3\dfrac{\vec u}{\|\vec u\|}=\dfrac{(-1,2,-4)}{\sqrt7}[/tex]
