IB DP Physics: SL复习笔记1.3.2 Combining & Resolving Vectors

Combining & Resolving Vectors

  • Vectors are represented by an arrow
    • The arrowhead indicates the direction of the vector
    • The length of the arrow represents the magnitude

Combining Vectors

  • Vectors can be combined by adding or subtracting them to produce the resultant vector
    • The resultant vector is sometimes known as the ‘net’ vector (eg. the net force)
  • There are two methods that can be used to combine vectors: the triangle method and the parallelogram method
  • To combine vectors using the 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
  • To combine vectors using the 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

Worked Example

Draw the vector c = a + b


Worked Example

Draw the vector c = a – b


Resolving Vectors

  • Two vectors can be represented by a single resultant vector
    • Resolving a vector is the opposite of adding vectors
  • A single resultant vector can be resolved
    • This means it can be represented by two vectors, which in combination have the same effect as the original one
  • When a single resultant vector is broken down into its parts, those parts are called components
  • For example, a force vector of magnitude F and an angle of θ to the horizontal is shown below


The resultant force F at an angle θ to the horizontal

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


The resultant force F can be split into its horizontal and vertical components

  • For the horizontal component, Fx = F cos θ
  • For the vertical component, Fy = F sin θ

Worked Example

A hiker walks a distance of 6 km due east and 10 km due north.

Calculate the magnitude of their displacement and its direction from the horizontal.


Step 4: State the final answer complete with direction

R = 2√34 = 11.66 = 12 km

θ = 59° east and upwards from the horizontal