Question

Let u = <-4, 3>. Find the unit vector in the direction of u, and write your answer in component form.

Answer 1

$\bf \textit{unit vector of }\ \textless \ a,b\ \textgreater \ \implies \left( \cfrac{1}{||\ \textless \ a,b\ \textgreater \ ||} \right)\ \textless \ a,b\ \textgreater \ \\\\ -------------------------------\\\\ u=\ \textless \ -4,3\ \textgreater \ \qquad \textit{unit vector}\implies \left( \cfrac{1}{||\ \textless \ -4,3\ \textgreater \ ||} \right)\ \textless \ -4,3\ \textgreater \ \\\\\\ \left( \cfrac{1}{\sqrt{(-4)^2+(3)^2}} \right)\ \textless \ -4,3\ \textgreater \ \implies \cfrac{1}{\sqrt{25}}\ \textless \ -4,-3\ \textgreater \ \implies \cfrac{1}{5}\ \textless \ -4,3\ \textgreater \ \\\\\\ \left\ \textless \ \cfrac{-4}{5}\quad ,\quad \cfrac{3}{5} \right\ \textgreater \ \impliedby \textit{same angle, same direction}$