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Vector
Subject:	Applied Mathematics & Mathematics
Level	Ordinary & Honours

A physical quantity that has both magnitude and direction is known as a Vector. An example of such is displacement. A specific type of notation is used to represent a vector in the plane and to denote a vector quantity: an arrow is placed above the representative letter etc.

The length of the vector is a representation of its magnitude - the vector with the longer length has a greater magnitude in the diagram above.

Addition

Vectors can be added using the so-called Parallelogram Method which is illustrated in the following diagram:

A vector is drawn from the tip of each vector parallel to the other, forming a parallelogram. The vector that is equal to the sum of the vectors is the vector from their common origin to the top of the parallelogram.

The i and j notation

When considering vectors in the cartesian plane, the axis are modified to vectors rather than the regular scalar x-y planes. The x-axis becomes the axis and the y-axis becomes the axis. It is important to note that almost all questions on the applied mathematics exam paper will use this notation and students must therefore be familiar with it.