Find the unit vector having the same direction as v.
-$$v = - 12 i + 5 j$$
A) $\mathbf { u } = - \frac { 12 } { 13 } \mathbf { i } + \frac { 5 } { 13 } \mathrm { j }$
B) $\mathbf { u } = - \frac { 13 } { 12 } \mathbf { i } + \frac { 13 } { 5 } \mathbf { j }$
C) $u = - \frac { 5 } { 13 } \mathrm { i } + \frac { 12 } { 13 } \mathrm { j }$
D) $\mathbf { u } = - 156 \mathbf { i } + 65 \mathrm { j }$

Question

Quizplus · Accepted Answer

To find the unit vector in the same direction as $v = - 12 i + 5 j$, you divide each component by the magnitude of $v$. The magnitude of $v$ is $\sqrt{(-12)^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13$. Thus, the unit vector is $\mathbf{u} = \frac{-12}{13}\mathbf{i} + \frac{5}{13}\mathbf{j}$.

Find the Unit Vector Having the Same Direction as V v=−12i+5jv = - 12 i + 5 jv=−12i+5j

Find the Unit Vector Having the Same Direction as V $v = - 12 i + 5 j$