Vectors

A vector has a length and a direction. A vector has a head and a tail.

If we put a vector on graph paper then we will want to know the location of the tail.

The sum of two vectors is a vector.

If we add two vectors together, we draw the first on graph paper with its tail at the origin, then we draw the second vector, placing its tail at the head of the first vector. We draw a vector from the origin to the head of the second factor and this vector is the sum of the two vectors.

Vector Components

(a,0) + (0,b) = (a,b)

In the above example, the vector is the sum of its components.

Two nonzero vectors are said to be collinear or linearly dependent if one is the other multiplied by a constant.

Example: (1,2) and (2,4)

Appendix A

Vectors and One-forms are related…