Find the unit vector having the same direction as v.
-$$v = - 3 i + j$$
A) $\mathbf { u } = - \frac { 3 \sqrt { 10 } } { 10 } \mathrm { i } - \frac { \sqrt { 10 } } { 10 } \mathrm { j }$
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 $v = -3i + j$, first calculate the magnitude of $v$, which is $\sqrt{(-3)^2 + 1^2} = \sqrt{9 + 1} = \sqrt{10}$. Then, divide each component of $v$ by its magnitude to get the unit vector: $\mathbf{u} = \frac{-3}{\sqrt{10}}i + \frac{1}{\sqrt{10}}j = -\frac{3\sqrt{10}}{10}i + \frac{\sqrt{10}}{10}j$.

Find the Unit Vector Having the Same Direction as V v=−3i+jv = - 3 i + jv=−3i+j

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