Respuesta :

Remember that

To find a unit vector with the same direction as a given vector, we divide the vector by its magnitude

The given vector is v=i-5j

Find out the magnitude

[tex]\begin{gathered} \lvert v\rvert=\sqrt[]{(1)^2+(-5)^2} \\ \lvert v\rvert=\sqrt[]{26} \end{gathered}[/tex]

Find out the unit vector

[tex]U_v=\frac{1}{\sqrt[]{26}}i-\frac{5}{\sqrt[]{26}}j[/tex]

Simplify the radicals in the denominator

so

[tex]\begin{gathered} U_v=\frac{\sqrt[]{26}}{\sqrt[]{26}}\cdot\frac{1}{\sqrt[]{26}}i-\frac{\sqrt[]{26}}{\sqrt[]{26}}\cdot\frac{5}{\sqrt[]{26}}j \\ U_v=\frac{\sqrt[]{26}}{26}i-\frac{5\sqrt[]{26}}{26}j \end{gathered}[/tex]

the answer is

[tex]U_v=\frac{\sqrt[]{26}}{26}i-\frac{5\sqrt[]{26}}{26}j[/tex]