Question

please help me solve this problem. I am familiar with this concept but im not sure what the process to solve is

Answer 1

v = 1/5 ( 3i - 4j)

Step-by-step explanation:

A unit vector is a vector whose magnitude is 1.

The unit vector is given by

`\hat{v}=\frac{\vec{v}}v`

where |v| is the magnitude of the vector.

Now in our case, we have

`\vec{v}=3\hat{i}-4\hat{j}`

The magnitude of the above vector

`|\hat{v}|=\sqrt[]{3^2+4^2}`
`=\sqrt[]{9+16}`
`=\sqrt[]{25}=5`

Hence,

`|\hat{v}|=5`

therefore, the unit vector is

`\vec{v}=\frac{3\hat{i}-4\hat{j}}{5}`

or to write it another way

`\boxed{\hat{v}=(1)/(5)(3\hat{i}-4\hat{j})\text{.}}`