How do vectors work in maths

Vectors Calculating the Modulus of a Vector. In this section, you will learn how to calculate the modulus of a vector. The modulus is a mathematical term for the length or the magnitude. This video and text below takes a look at Vectors and Scalars. Zero vector and unit vectors. Inverse Vectors. Vector addition and subtraction.

And we have this rounded result:. And it looks like this for Sam and Alex:. Example: A plane is flying along, pointing North, but there is a wind coming from the North-West.

If you watched the plane from the ground it would seem to be slipping sideways a little. Example: k b is actually the scalar k times the vector b. We can think of vectors as points in a coordinate system corresponding to points in space, or we can think of vectors as objects with magnitude and direction. In this article we attempt to clarify why there are two definitions of vectors and relate the two. The most perceptive and mathematically able school students often feel they don't understand the use of vectors and they are absolutely right to question this because school textbooks often switch between the different sorts of vectors without justifying what they are doing.

Vectors are usually first introduced as objects having magnitude and direction, for example translations, displacements, velocities, forces etc.

Vectors defined this way are called free vectors. If we simply specify magnitude and direction then any two vectors of the same length and parallel to each other are considered to be identical. So by this definition a vector is an infinite set of parallel directed line segments.

For example consider the translation three units across and one unit up. You can draw your own diagrams to illustrate this. A translation of the plane moves all the points of the plane simultaneously by the same translation vector, so we can think of a free vector as the same thing as a translation.

You can explore the concept of the magnitude and direction of a vector using the below applet. Note that moving the vector around doesn't change the vector, as the position of the vector doesn't affect the magnitude or the direction.

But if you stretch or turn the vector by moving just its head or its tail, the magnitude or direction will change.

This applet also shows the coordinates of the vector, which you can read about in another page. The magnitude and direction of a vector. The two defining properties of a vector, magnitude and direction, are illustrated by a red bar and a green arrow, respectively.

More information about applet. There is one important exception to vectors having a direction. Since it has no length, it is not pointing in any particular direction. There is only one vector of zero length, so we can speak of the zero vector.