    Next: Scalars and Vectors Up: Mathematical Physics Previous: Complex Numbers   Contents

# Vectors and Vector Products

A vector is a quantity with dimensions, a magnitude, and a direction relative to a specific coordinate frame. Note that it isn't sufficient to have a list of (say) three numbers labelled , , and - the components have to transform when the underlying coordinate frame is transformed like a vector''. Although there are multiple coordinate systems in which vectors can be expressed, the simplest'' one is Cartesian, where a vector can typically be written: in terms of component scalar amplitudes and unit vectors in the orthogonal directions . The resultant is also the result of a geometric triangle or parallelogram rule:

vector-sum.eps

Subtraction is just addition of a negative: It can also be visualized by means of a geometric triangle so that .

vector-difference.eps

Subsections    Next: Scalars and Vectors Up: Mathematical Physics Previous: Complex Numbers   Contents
Robert G. Brown 2017-07-11