How to Add Geometric Vectors

You can add two free geometric vectors using the parallelogram method by positioning both vectors at the same origin (O).

A Practical Example

On a plane, two geometric vectors, AB and CD, belong to different equivalence classes.

To add them, I reposition both vectors so they share the same origin.

Once aligned, the vectors AB and CD, now originating from O, become OB and OD.

Which origin should you choose? If the plane has a designated origin O, using it is the best choice as it simplifies calculations.

Now, I add the two vectors OB and OP using the parallelogram method.

The sum of vectors OB and OD results in vector OP.

In conclusion, vector OP represents the equivalence class of the free geometric vector AB + CD.

When applied at every point on the plane, vector OP defines the free geometric vector OP.