Question

How do you normalize `(-5i + 12j+ 2 k)`?

Answer 1

Normalizing a vector means making a unit vector in the same direction by dividing each component of the vector by the length of the original vector. In this case the normalized vector is `(−5/sqrt(173)i+12/sqrt(173)j+2/sqrt(173)k)`

Explanation:

First find the length of the vector. If a vector is `(ai+bk+cj)` its length is given by:

`l=sqrt(a^2+b^2+c^2`

The length of the given vector, `(−5i+12j+2k)`, is:

`l=sqrt((-5)^2+12^2+2^2) =sqrt(173) =13.2`

We can express the normalized vector in two equivalent ways:

`(−5/sqrt(173)i+12/sqrt(173)j+2/sqrt(173)k)`

OR

`(−5/13.2i+12/13.2j+2/13.2k)`