## Translating a Vector

Translating a vector is quite different than rotating a vector. For translation to occur, the transformation matrix must be altered with an additional row and column. For example, An identity matrix allowing translation is represented by a 4x4 matrix as follows:

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

wcomponent 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)