Question

Find the unit vector in the same direction as vv=i-5jU=?

Answer 1

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

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

Find out the unit vector

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

Simplify the radicals in the denominator

so

`\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}`

the answer is

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