?Find a unit vector in the direction of $\mathbf { w } = \langle - 4 , - 6 \rangle$ . ?
A)? $\left\langle - \frac { 2 \sqrt { 13 } } { 13 } , - \frac { 3 \sqrt { 13 } } { 13 } \right\rangle$
B)? $\left\langle - \frac { \sqrt { 13 } } { 39 } , - \frac { \sqrt { 13 } } { 26 } \right\rangle$
C)? $\left\langle - \frac { \sqrt { 13 } } { 4 } , - \frac { \sqrt { 13 } } { 6 } \right\rangle$
D)? $\left\langle - \frac { \sqrt { 13 } } { 13 } , - \frac { \sqrt { 13 } } { 13 } \right\rangle$
E)? $\left\langle - \frac { 8 \sqrt { 13 } } { 13 } , - \frac { 12 \sqrt { 13 } } { 13 } \right\rangle$

Question

Quizplus · Accepted Answer

To find a unit vector in the direction of $\mathbf{w} = \langle -4, -6 \rangle$, you first calculate the magnitude of $\mathbf{w}$, which is $\sqrt{(-4)^2 + (-6)^2} = \sqrt{16 + 36} = \sqrt{52} = \sqrt{4 \cdot 13} = 2\sqrt{13}$. Then, divide each component of $\mathbf{w}$ by its magnitude to get the unit vector: $\left\langle \frac{-4}{2\sqrt{13}}, \frac{-6}{2\sqrt{13}} \right\rangle = \left\langle -\frac{2\sqrt{13}}{13}, -\frac{3\sqrt{13}}{13} \right\rangle$.

?Find a Unit Vector in the Direction Of w=⟨−4,−6⟩\mathbf { w } = \langle - 4 , - 6 \ranglew=⟨−4,−6⟩

?Find a Unit Vector in the Direction Of $\mathbf { w } = \langle - 4 , - 6 \rangle$