# How do you find the unit vector of 5i-12j?

Jul 28, 2016

$\frac{5}{13} i - \frac{12}{13} j$

#### Explanation:

The normalised vector corresponding to $5 i - 12 j$ is $\frac{5}{13} i - \frac{12}{13} j$

To find the normalised vector, divide by the (Euclidean) norm of the vector:

$| | 5 i - 12 j | | = \sqrt{{5}^{2} + {12}^{2}} = \sqrt{25 + 144} = \sqrt{169} = 13$

So the unit vector in the same direction is:

$\frac{1}{13} \left(5 i - 12 j\right) = \frac{5}{13} i - \frac{12}{13} j$