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Vectors
What are vectors?
A vector is a type of number that has both a size and a direction
Here we only deal with two-dimensional vectors, although it is possible to have
vectors with any number of dimensions
Representing vectors
Vectors are represented as arrows, with the arrowhead indicating the direction of the
vector, and the length of the arrow indicating the vector’s magnitude (ie its size)
In print vectors are usually represented by bold letters (as with vector a
in the diagram above), although in handwritten workings underlined
letters are normally used, a.
Another way to indicate a vector is to write its starting and ending points with an
arrow symbol over the top.
Vectors and transformation geometry
In transformation geometry, translations are indicated in the form of a column vector:
Vectors on a grid
You also need to be able to work with vectors on their own, outside of the
transformation geometry context
When vectors are drawn on a grid (with or without x and y axes), the vectors can be
represented in the same (x y) column vector form as above
Multiplying a vector by a scalar
A scalar is a number with a magnitude but no direction – ie the regular numbers you
are used to using
When a vector is multiplied by a positive scalar, the magnitude of the vector
changes, but its direction stays the same