Find the vector v that has a magnitude of 4 and is in the same direction as u, where $$\mathbf { u } = \langle - 5 , - 3 \rangle \text {. }$$
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 $\mathbf{u} = \langle -5, -3 \rangle$ is $\sqrt{(-5)^2 + (-3)^2} = \sqrt{25 + 9} = \sqrt{34}$. To get a vector with a magnitude of 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 That Has a Magnitude of 4 u=⟨−5,−3⟩. \mathbf { u } = \langle - 5 , - 3 \rangle \text {. }u=⟨−5,−3⟩.

Find the Vector V That Has a Magnitude of 4 $\mathbf { u } = \langle - 5 , - 3 \rangle \text {. }$