Question

How do you find a unit vector in the same direction as a=(-10, 6, -7)?

Answer 1

Compute the magnitude and then divide each component by the magnitude.

Explanation:

Compute the magnitude:

`|veca|= sqrt((-10)^2+ 6^2+ (-7)^2)`

`|veca|= sqrt(100 + 36+ 49)`

`|veca|= sqrt(185)`

To obtain the unit vector of `veca = (-10, 6, -7)`, we divide each component by `sqrt185` but we should rationalize `1/sqrt185` to `sqrt185/185`:

`hata = ( (-10sqrt185)/185, (6sqrt185)/185, (-7sqrt185)/185)`