Scalars & Vectors
- A scalar is a quantity which only has a magnitude (size)
- A vector is a quantity which has both a magnitude and a direction
- For example, if a person goes on a hike in the woods to a location which is a couple of miles from their starting point
- As the crow flies, their displacement will only be a few miles but the distance they walked will be much longer
Displacement is a vector while distance is a scalar quantity
- Distance is a scalar quantity because it describes how an object has travelled overall, but not the direction it has travelled in
- Displacement is a vector quantity because it describes how far an object is from where it started and in what direction
- Some common scalar and vector quantities are shown in the table below:
Scalars and Vectors Table
Vector Notation
The arrow on vector notation does not indicate an actual direction, just that the quantity has a direction
- This means writing the quantity to make it clear that it is a vector
- In text books vectors are often shown as bold and italic, for example F or s
- Another form of notation, and easier to do in handwriting, is putting an arrow over the top of the quantity, for example or
- The arrow does not indicate the actual direction of the vector, only that is has a direction
Exam Tip
Do you have trouble figuring out if a quantity is a vector or a scalar? Just think - can this quantity have a minus sign? For example - can you have negative energy? No. Can you have negative displacement? Yes!