Question

How do you normalize `(15i- 3j + 12k)`?

Answer 1

Normalizing a vector involves dividing each of its elements by its length. In this case the normalized vector is `(15/sqrt378i-3/sqrt378j+12/sqrt378k)` or `(15/19.4i-3/19.4j+12/19.4k)`.

Explanation:

Normalizing a vector is creating a vector of length `1` unit in the same direction as the original vector.

To do that, we divide each of the elements by the length of the vector. The find the length of a vector `(ai+bj+ck)` the formula is:

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

In this case:

`l = sqrt(15^2+(-3)^2+12^2)=sqrt(225+9+144) = sqrt378` `(=19.4)`

The final vector can be expressed as `(15/sqrt378i-3/sqrt378j+12/sqrt378k)` or `(15/19.4i-3/19.4j+12/19.4k)`.