What information do you need to fully define a vector?
What information do you need to
fully define a vector? Let’s begin by considering the
two-dimensional 𝑥𝑦 plane as shown. The arrow drawn represents a
vector. There are two ways that we could
define this. Firstly, any vector has both
magnitude and direction. The length of the line segment
drawn is the magnitude of the vector, and the arrow indicates the direction. The start point for a vector is
sometimes known as its tail, and the endpoint is known as the head. The direction of any vector is,
therefore, from its tail to its head. This means that we also have a
second way of defining a vector if we know its initial point or tail and terminal
point or head. We can, therefore, conclude that
there are two pieces of information that we need to define a vector, either its
magnitude and direction or its initial and terminal points.