Question

How do you normalize `(- 2i - j - k)`?

Answer 1

`hatv = -sqrt(2/3)hati - 1/(sqrt6)hatj - 1/(sqrt6)hatk`

Explanation:

Normalization of a vector is the process of finding a unit vector in the same direction of the vector in question.

The equation for the normalization of a vector (which I'll call `vecv`) is given by

`(vecv)/(||vecv||)`

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

The magnitude of `vecv` is

`||vecv|| = sqrt((-2)^2 + (-1)^2 + (-1)^2) = color(red)(ul(sqrt6`

Thus, the unit vector (`hatv`) will be

`hatv = (-2)/(color(red)(sqrt6))hati - 1/(color(red)(sqrt6))hatj - 1/(color(red)(sqrt6))hatk`

`color(blue)(ulbar(|stackrel(" ")(" "hatv = -sqrt(2/3)hati - 1/(sqrt6)hatj - 1/(sqrt6)hatk" ")|)`