Question

How do you find a unit vector in the direction of v: v = - 5i + 2j?

Answer 1

`-5/sqrt29i+2/sqrt29j`.

Explanation:

A unit vector in the direction of `vecv`, is denoted by `hat(vecv)`,

and, is defined by,

`hat(vecv)=vecv/||vecv||", provided, "vecvnevec0`.

Here, `vecv=-5i+2j=(-5,2) nevec0`

`rArr ||vecv||=sqrt{(-5)^2+(2)^2}=sqrt29`.

`:. hat(vecv)=-5/sqrt29i+2/sqrt29j`.