Question

How do you normalize `(-300i + 200j - 150k)`?

Answer 1

The normalised vector is: `((-300/390.5)i+(200/390.5)j-(150/390.5)k)`, which can also be expressed as `(-0.77i+0.51j-0.38k)`

Explanation:

Normalising a vector involves dividing each of its elements by the length of the vector. This yields a vector in the same direction as the original vector, but one unit in length.

First we find the length of the vector:

`l=sqrt((-300)^2+200^2+(-150)^2)=sqrt(90000+40000+22500)`
`=sqrt(152500)~~390.5` `units`

The normalised vector, then, is:

`((-300/390.5)i+(200/390.5)j-(150/390.5)k)`