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Unless the stranger has a GPS receiver, the city block coordinate frame is likely to be the most useful.

Representing Vectors with Column Matrices

Virutal world and two coordinate frames

Back to our exciting virtual world. The displacement from point A to point B is the vector v. The vector does not depend on any coordinate system. Using the first coordinate system (middle diagram) the displacement is represented as

(difference in x coordinates, difference in y coordinates)

In the diagram this is (4, 0)T. Moving 4 units from point A in the direction of the x axis brings us to point B. In the second coordinate system (right diagram) the same vector is represented by (2.8, -1.4)T.


Both points and vectors are represented with column matrices. Is this likely to be confusing?