Find the unit vector having the same direction as v.
-$$\mathbf { v } = - 3 \mathbf { i } + \mathbf { j }$$
A) $\mathbf { u } = - \frac { 3 \sqrt { 10 } } { 10 } \mathbf { i } - \frac { \sqrt { 10 } } { 10 } \mathbf { j }$
B) $\mathbf { u } = - \frac { \sqrt { 10 } } { 3 } \mathbf { i } + \sqrt { 10 } \mathbf { j }$
C) $\mathbf { u } = - 3 \sqrt { 10 } \mathbf { i } + \sqrt { 10 } \mathbf { j }$
D) $\mathbf { u } = - \frac { 3 \sqrt { 10 } } { 10 } \mathbf { i } + \frac { \sqrt { 10 } } { 10 } \mathbf { j }$

Question

Quizplus · Accepted Answer

To find the unit vector in the same direction as $\mathbf{v} = -3\mathbf{i} + \mathbf{j}$, we first calculate the magnitude of $\mathbf{v}$, which is $\sqrt{(-3)^2 + 1^2} = \sqrt{9 + 1} = \sqrt{10}$. The unit vector $\mathbf{u}$ is then obtained by dividing each component of $\mathbf{v}$ by its magnitude, resulting in $\mathbf{u} = \frac{-3}{\sqrt{10}}\mathbf{i} + \frac{1}{\sqrt{10}}\mathbf{j}$, which simplifies to $\mathbf{u} = -\frac{3\sqrt{10}}{10}\mathbf{i} + \frac{\sqrt{10}}{10}\mathbf{j}$.

Find the Unit Vector Having the Same Direction as V v=−3i+j\mathbf { v } = - 3 \mathbf { i } + \mathbf { j }v=−3i+j

Find the Unit Vector Having the Same Direction as V $\mathbf { v } = - 3 \mathbf { i } + \mathbf { j }$