A Student Guide to A-Level Mathematics

Vectors Have a Magnitude and a Direction

A vector describes a magnitude and a direction.

What’s Magnitude?

A magnitude is a number, describing the size of something. It does not describe any direction.

“A car is travelling \(80 \text{km}/\text{h}\).”

This information, “\(80 \text{km}/\text{h}\),” is not a vector because it doesn’t describe it’s direction.

The “\(80 \text{km}/\text{h}\)” is a magnitude, which in this case is called “speed”.


If instead, we said “The car is travelling \(80 \text{km}/\text{h}\) east”, then this information is a vector, because we’ve described both the direction in which the car travels and the magnitude of how fast it travels.

This vector in this case is called “velocity”. Speed is only a magnitude, but velocity is a vector. Speed is the magnitude of the velocity.

Quick! More Examples!

Moving \(5 \mathrm{m}\) is not a vector.

Moving, to the right, is not a vector.

Moving \(5 \mathrm{m}\) to the right is a vector.

“\(5 \mathrm{m}\)” is the magniude.

“to the right” is the direction.


How much you weigh is not a vector.


“Remote control is a metre away” does not describe a vector.

“Remote control is in front of me” does not describe a vector.

“Remote control is a metre in front of me” describes a vector.

“a metre” is the magnitude, and “infront of me” is the direction.