[tex]\text{unit vector = u= <}\frac{3}{5},\frac{-4}{5}>[/tex]Explanation:
v = <3, -4>
[tex]\begin{gathered} \text{unit vector = u = }\frac{v}{\mleft\Vert v\mright|\text{|}} \\ v\text{ = <3, -4>} \\ \mleft\Vert\text{ v }\mright|\text{| = }\sqrt[\text{ }]{(3)^2+(-4)^2\text{ }}\text{ =}\sqrt[]{9+16} \\ \Vert\text{ v }|\text{| =}\sqrt[]{25} \\ \Vert\text{ v }|\text{| = 5} \end{gathered}[/tex][tex]\begin{gathered} \text{ u = }\frac{<3,\text{ -4>}}{5} \\ unit\text{ vector = <}\frac{3}{5},\frac{-4}{5}> \end{gathered}[/tex]
Verifying || u || = 1
[tex]\begin{gathered} \text{unit vector = u= <}\frac{3}{5},\frac{-4}{5}> \\ \mleft\Vert\text{ u }\mright|\text{|= }\sqrt[]{(\frac{3}{5})^2+(\frac{-4}{5}})^2 \\ =\text{ }\sqrt[]{\frac{9}{25}+\frac{16}{25}}\text{ =}\sqrt[]{\frac{9+16}{25}} \\ \mleft\Vert u\text{ }\mright|\text{| = }\sqrt[]{\frac{25}{25}} \\ \Vert u\text{ }|\text{| =}1 \end{gathered}[/tex]
