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

Question

Quizplus · Accepted Answer

The unit vector $\mathbf{u}$ in the same direction as $\mathbf{v} = -12\mathbf{i} + 5\mathbf{j}$ is found by dividing $\mathbf{v}$ by its magnitude. The magnitude of $\mathbf{v}$ is $\sqrt{(-12)^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13$. Thus, $\mathbf{u} = \frac{\mathbf{v}}{|\mathbf{v}|} = \frac{-12\mathbf{i} + 5\mathbf{j}}{13} = -\frac{12}{13}\mathbf{i} + \frac{5}{13}\mathbf{j}$.

Find the Unit Vector Having the Same Direction as V v=−12i+5j\mathbf { v } = - 12 \mathbf { i } + 5 \mathbf { j }v=−12i+5j

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