Answer:
The unit vector in component form is [tex]\hat{u} = \left(\frac{2}{\sqrt{13} },-\frac{3}{\sqrt{13}} \right)[/tex] or [tex]\hat{u} = \frac{2}{\sqrt{13}}\,i-\frac{3}{13}\,j[/tex].
Step-by-step explanation:
Let be [tex]\vec u = (2,-3)[/tex], its unit vector is determined by following expression:
[tex]\hat {u} = \frac{\vec u}{\|\vec u \|}[/tex]
Where [tex]\|\vec u \|[/tex] is the norm of [tex]\vec u[/tex], which is found by Pythagorean Theorem:
[tex]\|\vec u\|=\sqrt{2^{2}+(-3)^{2}}[/tex]
[tex]\|\vec u\| = \sqrt{13}[/tex]
Then, the unit vector is:
[tex]\hat{u} = \frac{1}{\sqrt{13}} \cdot (2,-3)[/tex]
[tex]\hat{u} = \left(\frac{2}{\sqrt{13} },-\frac{3}{\sqrt{13}} \right)[/tex]
The unit vector in component form is [tex]\hat{u} = \left(\frac{2}{\sqrt{13} },-\frac{3}{\sqrt{13}} \right)[/tex] or [tex]\hat{u} = \frac{2}{\sqrt{13}}\,i-\frac{3}{13}\,j[/tex].
