Some physical quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation of quantities.

  • Vectors are quantities with magnitude and direction that can be represented by arrows. The length of the arrow is proportional to the magnitude and the direction is the same as the direction of the quantity (e.g., displacement).
  • Scalars are quantities with magnitude but not direction.
    Vectors Scalars
    displacement distance
    velocity speed
    acceleration energy/work
    force power
  • To add two vectors arrange them nose-to-tail and draw a line connecting the free tail to the free nose.

    $\rm \color{red}{a} + \color{cornflowerblue}{b} = \color{green}{c}$
  • To subtract two vectors, reverse the direction of the vector which is subtracted:
    Topic-113
  • A vector $\rm V$ can be broken down into two perpendicular components: $\rm V\sin\theta$ and $\rm V\sin\theta$