# How do you find the unit vector having the same direction as vector u=3i-4j?

Jul 28, 2016

Unit vector $\to \frac{3}{5} i - \frac{4}{5} j$

#### Explanation:

This question type is asking: What would the value of i and j be if the vector length was 1.

Current vector length is $\text{ } \sqrt{{3}^{3} + {\left(- 4\right)}^{2}} = \sqrt{25} = 5$

The | | notation means 'Cardinality' which is another name for magnitude. So

$| 3 i - 4 j | = 5$ but we need a length of 1 so

unit vector $= | \frac{3 i}{5} - \frac{4 j}{5} | = \frac{5}{5} = 1$