Question

Does anyone know how to find the unit vector of: v: <-6, -8> ?

It's either,
A.) <3/5, 4/5 >
B. <-3/5, -4/5 >
C.) <4/5, 3/5 >
D.) <-4/5, -3/5 >
Thanks.

Answer 1

the unit vector, or a vector on the Unit Circle, has a magnitude of 1, thus is called a Unit vector :), in the Unit Circle, and is coterminal with hmm in this case -6,-8, which has a bigger magnitude than 1


`\bf \begin{array}{ccccllll} \ \textless \ &-6&,&-8\ \textgreater \ \\ &a&&b \end{array}\qquad \textit{so the vector }v\textit{ magnitude is} \\\\\\ ||v||=√(a^2+b^2)\implies ||v||=√((-6)^2+(-8)^2)\implies ||v||=10 \\\\\\ \textit{thus the unit vector }v_o\textit{ will be}\implies \left((a)/(||v||), (b)/(||v||) \right) \\\\\\ or\implies \left( (-6)/(10),(-8)/(10) \right)\implies \left( (-3)/(5),(-4)/(5) \right)`