Find a unit vector that has the same direction as the vector $\langle6 , - 8 \rangle$ .
A) $\langle \frac { 4 } { 5 } , \frac { 3 } { 5 } \rangle$
B) $\left( \frac { 3 } { 5 } , \frac { 4 } { 5 } \right)$
C) $\left( \frac { 1 } { 3 } , \frac { 1 } { 4 } \right)$
D) $( 4 , - 3 )$
E) $\left( - \frac { 3 } { 5 } , - \frac { 4 } { 5 } \right)$
F) $\left( - \frac { 3 } { 5 } , \frac { 4 } { 5 } \right)$
G) $\left( \frac { 3 } { 5 } , - \frac { 4 } { 5 } \right)$
H) $\langle 6 , - 8 \rangle$

Question

Find a unit vector that has the same direction as the vector $\langle6 , - 8 \rangle$ .
A) $\langle \frac { 4 } { 5 } , \frac { 3 } { 5 } \rangle$ 
B) $\left( \frac { 3 } { 5 } , \frac { 4 } { 5 } \right)$ 
C) $\left( \frac { 1 } { 3 } , \frac { 1 } { 4 } \right)$ 
D) $( 4 , - 3 )$ 
E) $\left( - \frac { 3 } { 5 } , - \frac { 4 } { 5 } \right)$ 
F) $\left( - \frac { 3 } { 5 } , \frac { 4 } { 5 } \right)$ 
G) $\left( \frac { 3 } { 5 } , - \frac { 4 } { 5 } \right)$ 
H) $\langle 6 , - 8 \rangle$

Quizplus · Accepted Answer

To find a unit vector in the same direction as $\langle6 , - 8 \rangle$, divide each component by the vector's magnitude. The magnitude is $\sqrt{6^2 + (-8)^2} = \sqrt{36 + 64} = \sqrt{100} = 10$. Thus, the unit vector is $\left( \frac{6}{10}, \frac{-8}{10} \right) = \left( \frac{3}{5}, -\frac{4}{5} \right)$.

Find a Unit Vector That Has the Same Direction as the Vector