# How do you find a unit vector from the point P=(1,1) Q=(5,4)?

unit vector$\to \hat{a} = \frac{4}{5} i + \frac{3}{5} j$
Let vector $\vec{a} = \vec{P Q} = \left(5 - 1\right) i + \left(4 - 1\right) j = 4 i + 3 j$
Then $| | a | | = \sqrt{{\left(5 - 1\right)}^{2} + {\left(4 - 1\right)}^{2}} = \sqrt{25} = 5$
So unit vector$\to \hat{a} = \frac{4}{5} i + \frac{3}{5} j$