Question

Let u = <-4, -3>. Find the unit vector in the direction of u, and write your answer in component form.

Answer 1

Given the vector
`\vec{u}=(-4,-3).`

This vector has the length

`|\vec{u}|=√((-3)^2+(-4)^2)=√(9+16)=√(25)=5.`

Let
`\vec{u}_0` be the unit vector in direction of
`\vec{u}.` If these vectors have the same directions, then they are collinear and, consequently,

`\frac{\vec{u}_0}{\vec{u}}=\frac{|\vec{u}_0|}{|\vec{u}|},\\ \\\frac{\vec{u}_0}{\vec{u}}=(1)/(5)\Rightarrow \vec{u}_0=\frac{\vec{u}}{5}=\left(-(3)/(5),-(4)/(5)\right).`