Syllabus Edition

First teaching 2014

Last exams 2024

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Combining & Resolving Vectors (DP IB Physics: SL)

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Katie M

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Katie M

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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

Vector Addition, downloadable IB Physics revision notes

Worked example

Draw the vector c = a – b

Vector Subtraction 1, downloadable IB Physics revision notesVector Subtraction 2, downloadable IB Physics revision notes

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

Representing Vectors, downloadable AS & A Level Physics revision notes

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

Resolving Vectors, downloadable AS & A Level Physics revision notes

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

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Katie M

Author: Katie M

Expertise: Physics

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.