This also implies that for a vector to be rotated/translated, the vector must also contain an additional component as follows:
The fourth component is sometimes refer to as the w component and must be set to 1.
Doing so, the vector will be able to be translated or rotated. For example, let's rotate vector u 90 degrees counterclockwise about the x-axis and translate it to point (2,1,3)
Hope it helps.