Question Video: Identifying the Information Needed to Define a Vector Mathematics • First Year of Secondary School

Video Transcript

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.