CIE AS Physics (9702) exams from 2022

Revision Notes

1.1.3 Scalars & Vectors

What are Scalar and Vector Quantities?

  • A scalar is a quantity which only has magnitude, while a vector is a quantity which has both magnitude and direction
  • For example, say you go on a hike in the woods to a location which is a couple of miles from your start point. As the crow flies, your displacement will only be a few miles but the distance you walked will be much longer


Displacement v distance, AS & A Level Physics revision notesDisplacement is a vector while distance is a scalar quantity

  • Distance is a scalar quantity because it describes how far you have travelled overall but not the direction. Whereas displacement is a vector quantity because it tells you how far you are from where you started and in what direction.
  • The table shows a variety of scalar and vector quantities you will come across in Physics:

Scalars and Vectors Table, AS & A Level Physics revision notes

Combining Vectors

  • Vectors are represented by an arrow to indicate its direction and length to represent its magnitude
  • We can combine vectors by adding or subtracting them from each other
  • There are two methods you can use to combine vectors: the triangle method and the parallelogram method
  • Triangle method:
    • Step 1: link the vectors head-to-tail
    • Step 2: the resultant vector is formed by connecting the tail of the first vector to the head of the second vector
  • Parallelogram method
    • Step 1: link the vectors tail-to-tail
    • Step 2: complete the resulting parallelogram
    • Step 3: the resultant vector is the diagonal of the parallelogram


Vector addition

Vector Addition, AS & A Level Physics revision notes


Vector subtraction

Vector Subtraction, AS & A Level Physics revision notes


Condition for equilibrium

Vector Equilibrium, AS & A Level Physics revision notesIf three forces acting on an object are in equilibrium; they form a closed triangle

Resolving Vectors

  • A force vector of magnitude F and an angle of θ to the horizontal is shown below

Representing Vectors, AS & A Level Physics revision notes



  • It is possible to resolve this vector into its horizontal and vertical components

Resolving Vectors, AS & A Level Physics revision notes

  •             Fx=Fcos θ
  •             Fy=Fsin θ

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