Scalar & Vector Quantities
- 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
- This is because it describes how an object has travelled overall, but not the direction it has travelled in
- Displacement is a vector quantity
- This is 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
Representing Vectors
- Vectors are represented by an arrow
- The arrowhead indicates the direction of the vector
- The length of the arrow represents the magnitude
The force vector F has both a direction and a magnitude
- Component vectors are sometimes drawn with a dotted line and a subscript indicating horizontal or vertical
- For example, Fx is the horizontal component and Fy is the vertical component of the force F
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!