Find the vector $\mathbf { v }$ that has a magnitude of 4 and is in the same direction as $\mathbf { u }$, where $\mathbf { u } = \langle - 5 , - 3 \rangle$.
A) $\mathbf { v } = \left\langle \frac { - 20 } { \sqrt { 34 } } , \frac { - 12 } { \sqrt { 34 } } \right\rangle$
B) $\mathbf { v } = \left\langle \frac { - 5 } { \sqrt { 34 } } , \frac { - 3 } { \sqrt { 34 } } \right\rangle$
C) $\mathbf { v } = \left\langle \frac { - 4 } { \sqrt { 34 } } , \frac { - 4 } { \sqrt { 34 } } \right\rangle$
D) $\mathbf { v } = \left\langle \frac { - 1 } { \sqrt { 34 } } , \frac { 1 } { \sqrt { 34 } } \right\rangle$
E) $\mathbf { v } = \left\langle \frac { 3 } { \sqrt { 34 } } , \frac { 5 } { \sqrt { 34 } } \right\rangle$

Question

Quizplus · Accepted Answer

To find a vector with a specific magnitude in the same direction as another vector, you scale the original vector by the ratio of the desired magnitude to the original magnitude. The magnitude of $\mathbf{u}$ is $\sqrt{(-5)^2 + (-3)^2} = \sqrt{25 + 9} = \sqrt{34}$. To get a vector of magnitude 4 in the same direction, multiply each component of $\mathbf{u}$ by $\frac{4}{\sqrt{34}}$, resulting in $\left\langle \frac{-20}{\sqrt{34}}, \frac{-12}{\sqrt{34}} \right\rangle$.

Find the Vector v\mathbf { v }v That Has a Magnitude of 4 and Is in the Magnitude

Find the Vector $\mathbf { v }$ That Has a Magnitude of 4 and Is in the Magnitude