Find the unit vector having the same direction as v.
-$$\mathbf { v } = - 30 \mathbf { i } + 30 \mathbf { j } - 15 \mathbf { k }$$
A) $\frac { \mathbf { v } } { \| v \| } = - \frac { 2 } { \sqrt { 5 } } \mathbf { i } + \frac { 2 } { \sqrt { 5 } } \mathbf { j } - \frac { 1 } { \sqrt { 5 } } \mathbf { k }$
B) $\frac { v } { \| v \| } = \frac { 2 } { 3 } i + \frac { 2 } { 3 } \mathrm { j } + \frac { 1 } { 3 } k$
C) $\frac { v } { \| v \| } = - \frac { 2 } { 9 } i + \frac { 2 } { 9 } j - \frac { 1 } { 9 } k$
D) $\frac { v } { \| v \| } = - \frac { 2 } { 3 } i + \frac { 2 } { 3 } \mathbf { j } - \frac { 1 } { 3 } k$

Question

Quizplus · Accepted Answer

The unit vector is found by dividing each component of vector v by its magnitude. The magnitude of v is $\sqrt{(-30)^2 + 30^2 + (-15)^2} = 45$. Thus, the unit vector is $-\frac{30}{45} \mathbf{i} + \frac{30}{45} \mathbf{j} - \frac{15}{45} \mathbf{k} = -\frac{2}{3} \mathbf{i} + \frac{2}{3} \mathbf{j} - \frac{1}{3} \mathbf{k}$.

Find the Unit Vector Having the Same Direction as V v=−30i+30j−15k\mathbf { v } = - 30 \mathbf { i } + 30 \mathbf { j } - 15 \mathbf { k }v=−30i+30j−15k

Find the Unit Vector Having the Same Direction as V $\mathbf { v } = - 30 \mathbf { i } + 30 \mathbf { j } - 15 \mathbf { k }$