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

Answer:

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

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

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