Scalar & Vector Quantities (HL IB Physics)

• 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, F_x is the horizontal component and F_y is the vertical component of the force F