Find the unit vector in the direction of the given vector. Write your answer in the indicated form.
-Let $\mathbf { u } = \langle 2,1 \rangle$. Find the unit vector in the direction of $\mathbf { u }$, and write your answer in component form.
A) $\langle 1,1 \rangle$
B) $\left( \frac { 2 } { 3 } , \frac { 1 } { 3 } \right)$
C) $\left| \frac { 2 } { \sqrt { 5 } } , \frac { 1 } { \sqrt { 5 } } \right|$
D) $\left( \frac { 2 } { 5 } , \frac { 1 } { 5 } \right)$

Question

Quizplus · Accepted Answer

To find the unit vector in the direction of $\mathbf { u } = \langle 2,1 \rangle$, you first calculate the magnitude of $\mathbf { u }$, which is $\sqrt{2^2 + 1^2} = \sqrt{5}$. Then, divide each component of $\mathbf { u }$ by its magnitude to get the unit vector: $\left( \frac { 2 } { \sqrt { 5 } } , \frac { 1 } { \sqrt { 5 } } \right)$.

Find the Unit Vector in the Direction of the Given u=⟨2,1⟩\mathbf { u } = \langle 2,1 \rangleu=⟨2,1⟩

Find the Unit Vector in the Direction of the Given $\mathbf { u } = \langle 2,1 \rangle$