Find a unit vector in the direction of the given vector. $\mathbf { u } = \langle - 6,6 \rangle$
A) $\langle 0,0 \rangle$
B) $\left\langle - \frac { \sqrt { 2 } } { 2 } , \frac { \sqrt { 2 } } { 2 } \right\rangle$
C) $\left\langle - \frac { \sqrt { 2 } } { 2 } , - \frac { \sqrt { 2 } } { 2 } \right\rangle$
D) $\left\langle \frac { \sqrt { 2 } } { 2 } , - \frac { \sqrt { 2 } } { 2 } \right\rangle$
E) $\left\langle \frac { \sqrt { 2 } } { 2 } , \frac { \sqrt { 2 } } { 2 } \right\rangle$

Question

Find a unit vector in the direction of the given vector.   $\mathbf { u } = \langle - 6,6 \rangle$  
A) $\langle 0,0 \rangle$
B)  $\left\langle - \frac { \sqrt { 2 } } { 2 } , \frac { \sqrt { 2 } } { 2 } \right\rangle$
C)  $\left\langle - \frac { \sqrt { 2 } } { 2 } , - \frac { \sqrt { 2 } } { 2 } \right\rangle$
D)  $\left\langle \frac { \sqrt { 2 } } { 2 } , - \frac { \sqrt { 2 } } { 2 } \right\rangle$
E)  $\left\langle \frac { \sqrt { 2 } } { 2 } , \frac { \sqrt { 2 } } { 2 } \right\rangle$

Quizplus · Accepted Answer

To find a unit vector in the direction of $\mathbf{u} = \langle -6, 6 \rangle$, we first find the magnitude of $\mathbf{u}$, which is $\sqrt{(-6)^2 + 6^2} = \sqrt{36 + 36} = \sqrt{72} = 6\sqrt{2}$. Then, we divide each component of $\mathbf{u}$ by its magnitude to get the unit vector: $\left\langle \frac{-6}{6\sqrt{2}}, \frac{6}{6\sqrt{2}} \right\rangle = \left\langle -\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right\rangle$.

Find a Unit Vector in the Direction of the Given u=⟨−6,6⟩\mathbf { u } = \langle - 6,6 \rangleu=⟨−6,6⟩

Find a Unit Vector in the Direction of the Given $\mathbf { u } = \langle - 6,6 \rangle$