Find the unit vector in the direction of u. $$\mathbf { u } = \{ - 5 , - 2 , - 1 \}$$
A) $\left( \frac { - 5 } { \sqrt { 30 } } , \frac { - 2 } { \sqrt { 30 } } , \frac { - 1 } { \sqrt { 30 } } \right)$
B) $\left( \frac { - 1 } { \sqrt { 30 } } , \frac { - 1 } { \sqrt { 30 } } , \frac { - 1 } { \sqrt { 30 } } \right)$
C) $\left( \frac { 5 } { \sqrt { 30 } } , \frac { 2 } { \sqrt { 30 } } , \frac { 1 } { \sqrt { 30 } } \right)$
D) $\left( \frac { 25 } { \sqrt { 30 } } , \frac { 4 } { \sqrt { 30 } } , \frac { 1 } { \sqrt { 30 } } \right)$
E) $\left( \frac { - 150 } { \sqrt { 30 } } , \frac { - 60 } { \sqrt { 30 } } , \frac { - 30 } { \sqrt { 30 } } \right)$

Question

Quizplus · Accepted Answer

To find the unit vector in the direction of $\mathbf{u}$, we need to divide $\mathbf{u}$ by its magnitude. The magnitude of $\mathbf{u}$ is $\|\mathbf{u}\|=\sqrt{(-5)^2+(-2)^2+(-1)^2}=\sqrt{30}$. Dividing each component of $\mathbf{u}$ by $\|\mathbf{u}\|$, we get the unit vector in the direction of $\mathbf{u}$: $\left( \frac { - 5 } { \sqrt { 30 } } , \frac { - 2 } { \sqrt { 30 } } , \frac { - 1 } { \sqrt { 30 } } ight)$. Therefore, the answer is choice $\boxed{	ext{(A)}}$.

Find the Unit Vector in the Direction of U u={−5,−2,−1}\mathbf { u } = \{ - 5 , - 2 , - 1 \}u={−5,−2,−1}

Find the Unit Vector in the Direction of U $\mathbf { u } = \{ - 5 , - 2 , - 1 \}$