Find the unit vector in the direction of the given vector. Write your answer in the indicated form.
-Let $\mathbf { u } = - 5 \mathbf { i } + 3 \mathbf { j }$. Find the unit vector in the direction of $\mathbf { u }$, and write your answer in component form.
A) $\left( - \frac { 5 } { 8 } , \frac { 3 } { 8 } \right)$
B) $\left( \frac { - 5 } { \sqrt { 34 } } , \frac { 3 } { \sqrt { 34 } } \right)$
C) $\langle 1,1 \rangle$
D) $\left( - \frac { 5 } { 34 } , \frac { 3 } { 34 } \right)$

Question

Quizplus · Accepted Answer

To find the unit vector in the direction of $\mathbf{u} = -5\mathbf{i} + 3\mathbf{j}$, you first calculate the magnitude of $\mathbf{u}$, which is $\sqrt{(-5)^2 + 3^2} = \sqrt{25 + 9} = \sqrt{34}$. Then, divide each component of $\mathbf{u}$ by its magnitude to get the unit vector: $\left( \frac{-5}{\sqrt{34}}, \frac{3}{\sqrt{34}} \right)$.

Find the Unit Vector in the Direction of the Given u=−5i+3j\mathbf { u } = - 5 \mathbf { i } + 3 \mathbf { j }u=−5i+3j

Find the Unit Vector in the Direction of the Given $\mathbf { u } = - 5 \mathbf { i } + 3 \mathbf { j }$