GCSE Maths (AQA)

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Splitting Vectors

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Geometry and Measures Vectors

Splitting Vectors

7:06 Vector Problem Solving
Spec R5 G25
Previous Collinear Points Next Vector Proofs
  • Vectors can be split into smaller vectors
  • Vector A can be split into vectors B and C
  • The sum of the smaller vectors equals the original vector
  • Vectors are added by joining them head to tail
  • Vector B and C, when joined head to tail, equal vector A
  • Smaller vectors can be expressed as scalar multiples of the original vector
  • B is equal to K times A, C is equal to L times A
  • K and L represent the scalar multipliers of A
  • The magnitude ratio of B to C can help determine K and L
  • K plus L equals 1
  • Example problem: vector V is split into vectors A to X and X to B
  • A to X equals K times V, X to B equals L times V
  • V equals A to X plus X to B
  • The ratio of K to L is given as 3 to 1
  • 3L equals K
  • K equals 3/4, L equals 1/4
  • Final expressions for the split vectors: AX equals 3/4 V, XB equals 1/4 V

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