Vectors
Vectors
Our very first topic is unusual in that we will start with a brief written presentation. More typically we will begin each topic with a videotaped lecture by Professor Auroux and follow that with a brief written presentation.
As we pointed out in the introduction, vectors will be used throughout the course. The basic concepts are straightforward, but you will have to master some new terminology. Another important point we made earlier is that we can view vectors in two different ways: geometrically and algebraically. We will start with the geometric view and introduce terminology along the way.
Geometric view
Geometric view
A vector is defined as having a magnitude and a direction. We represent it by an arrow in the plane or in space. The length of the arrow is the vector's magnitude and the direction of the arrow is the vector's direction.
In this way, two arrows with the same magnitude and direction represent the same vector.
One (same vector)
We will refer to the start of the arrow as the tail and the end as the tip or head.
The vector between two points will be denoted PQ.
We call P the initial point and Q the terminal point of PQ.
The magnitude of the vector A will be denoted absolute value A. Magnitude will also be called length or norm