Question

How do you normalize `<0, 1, 3>`?

Answer 1

`hatv = < 0, 1/(sqrt10), 3/(sqrt10) >`

Explanation:

Normalization of a vector is the process of finding a unit vector in the same direction of that vector (with magnitude (or "norm") `1`). It is found by the equation

`ulbar(|stackrel(" ")(" "hatv = (vecv)/(||vecv||)" ")|)`

where

`hatv` denotes the unit vector

`||vecv||` is the magnitude of vector `vecv`

The magnitude of `vecv` is given by

`||vecv|| = sqrt(0^2 + 1^2 + 3^2) = color(red)(ul(sqrt10`

Thus, we have

`hatv = (< 0,1,3 >)/(color(red)(sqrt10)) = color(blue)(ulbar(|stackrel(" ")(" "< 0, 1/(sqrt10), 3/(sqrt10) >" ")|)`