The University of Sydney - School of Mathematics and Statistics

What is a vector?	Page 1 of 4

A vector is a quantity with magnitude and a direction. The magnitude of the vector is also called its length.

Examples: velocity, acceleration, momentum, force, electric and magnetic field intensities.

A vector is represented by a directed line segment. The direction of the vector is indicated by an arrow pointing from the tail to the head.

If the tail is at point A and the head is at point B, the vector from A to B is written .

The length (magnitude) of a vector v is written |v|. The length is always a non-negative real number.

For example, we can draw a vector from corner A of a house to corner B. The vector has direction and length but exists independently of the house.

You get the same vector if you start at some other point C and then draw an arrow in the same direction as and with the same length as that of .

All that matters is the direction and magnitude of the vector; if these stay the same we are looking at the same vector, no matter where it appears. For an illustration, click the button below. The arrow moves but its direction and length remain the same, therefore it always represents the same vector.