Any vector can be expressed as a sum of other vectors. If you choose to express a particular vector as a sum of orthogonal vectors, then each of the vectors in the sum is the Vector Component of the original vector, in the direction it points.

For example, one could say that Busyville is 1.41 km Northwest of Happyland, or one could say that Busyville is 1 km North of Happyland and 1 km West of Happyland. In the latter case, "1 km North" and "1 km West" are the vector components in the North and West directions of the displacement between Busyville and Happyland.

The vector components need not be along some particular set of vectors. Consider Townsville, which is 1.41 km north of Busyville. One could say that Townsville is 1 km Northwest and 1 km Northeast of Busyville. Then "1 km Northwest" and "1km Northeast" are vector components of the displacement between Townsville and Busyville in the Northwest and Northeast directions.

One handy thing about the vector components is that as long as the vector components are orthogonal, the sum under quadrature of their magnitudes is the magnitude of the vector of which they are components. It is also possible to consider vector components of a vector which are not orthogonal, so long as they are linearly independent, but they will lose this handy property.

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