Scalars & vectors

• Scalars & Vectors

  • All quantities can be one of two types:
  • A scalar
  • A vector
• Scalars

  • Scalars are quantities that have only a magnitude
  • For example, mass is a scalar since it is a quantity that has magnitude without a direction
  • Distance is also a scalar since it only contains a magnitude, not a direction
• Vectors

  • Vectors have both magnitude and direction
  • Velocity, for instance, is a vector since it is described with both a magnitude and a direction
  • When describing the velocity of a car it is necessary to mention both its speed and the direction in which it is travelling
  • For example, the velocity might be 60 km per hour (magnitude) due west (direction)
  • Equivalently, the velocity might be –60 km per hour. In this case, the negative sign might indicate the car is travelling to the left, whereas a positive sign would indicate the opposite direction (to the right)
• • Some vectors and scalars are similar to each other
  • For example, the scalar quantity distance corresponds to the vector quantity displacement
  • The table below compares some vector and scalar quantities related to moving objects
• SCALARS & VECTORS:

  A) Distance

  B) Vector

  C) Scalar

  D) Velocity

  
• Difference between distance and displacement

  • Distance is a measure of how far an object travels
  • It is a scalar quantity - it has a size (magnitude), but the direction is not important
• • Displacement is a measure of how far something is from its starting position, along with its direction
  • It is a vector quantity - it describes both magnitude and direction