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

Question

Quizplus · Accepted Answer

The unit vector in the direction of v is found by dividing v by its magnitude. The magnitude of v is $\sqrt{(-30)^2 + 30^2 + (-15)^2} = 15\sqrt{5}$. Dividing each component by this magnitude gives the unit vector: $-\frac{2}{3}i + \frac{2}{3}j - \frac{1}{3}k$.

Find the Unit Vector Having the Same Direction as V v=−30i+30j−15kv = - 30 i + 30 j - 15 kv=−30i+30j−15k

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