1 Answer

Jondykeman · Answer 1 · 2021-10-06T09:53:58+0000

Step-by-step explanation:

In this exercise we have the following vector:

$\vec{v}=(8,-4)$

So we need to find a unit vector
$\vec{u}$ which is defined as follows:

$\vec{u}=\frac{\vec{v}}{\mid \vec{v} \mid}$

Finding the magnitude of the vector:

$\mid \vec{v} \mid=√((8)^2+(-4)^2) \\ \\ \mid \vec{v} \mid=√(64+16) \\ \\ \mid \vec{v} \mid=√(80) \\ \\ \mid \vec{v} \mid=4√(5)$

Then, by substituting the unit vector is:

$\vec{u}=((8,-4))/(4√(5)) \\ \\ \vec{u}=((8,-4))/(4√(5)) \\ \\ \vec{u}=((8)/(4√(5)),-(4)/(4√(5))) \\ \\$

$\vec{u}=((8)/(4√(5))(√(5))/(√(5)),-(4)/(4√(5))(√(5))/(√(5))) \\ \\ \\ \boxed{\vec{u}=\left((2√(5))/(5),-(5)/(√(5))\right)}$