# How do you find the unit vector having the same direction as vector a = 8i-15j?

$\hat{a} = \frac{8}{17} i - \frac{15}{17} j$.
Given a non-null vector $\vec{x}$, the unit vector in its direction, denoted by, $\hat{x}$ is given by, $\hat{x} = \frac{\vec{x}}{|} | \vec{x} | |$
As $| | \vec{a} | | = \sqrt{\left({8}^{2} + {\left(- 15\right)}^{2}\right)} = \sqrt{289} = 17$
Hence, $\hat{a} = \frac{1}{17} \left\{8 \left(\hat{i}\right) - 15 \left(\hat{j}\right)\right\} = \frac{8}{17} i - \frac{15}{17} j$.