GCSE Maths (Edexcel)
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Splitting Vectors
- 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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372
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18
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