# How do you normalize # (2i+j+2k) #?

##### 1 Answer

Jan 31, 2016

The normalized vector is

This is a unit vector in the same direction as the original vector.

#### Explanation:

Normalizing a vector involves dividing the coefficient of each of its elements by the length of the vector, to yield a unit vector (length =1) in the same direction as the original vector.

To do this we first need to find the length of the vector. If the vector is in the form

In this case this is:

Now we divide

The normalized vector is

This is a unit vector in the same direction as the original vector.