# Vector

## Key Stage 4

### Meaning

A vector is a quantity with both magnitude and direction.

Vector quantities include:

• Forces \(\overrightarrow{F}\) - A push or a pull which has a magnitude (size) and a direction.
• Displacement \(\overrightarrow{s}\) - The distance and direction from one point in space to another.
• Velocity \(\overrightarrow{v}\) - The speed and direction that an object is moving.
• Acceleration \(\overrightarrow{a}\) - The rate of change of velocity and the direction of this change.

If a quantity does not include direction, then it is called a scalar, not a vector.

### Representing Vectors

Vectors are written with either an underline (\(\underline{F}\),\(\underline{s}\),\(\underline{v}\),\(\underline{a}\)) or an arrow above (\(\overrightarrow{F}\),\(\overrightarrow{s}\),\(\overrightarrow{v}\),\(\overrightarrow{a}\)).
Vectors are often drawn on diagrams. They are drawn as an arrow because an arrow can show the magnitude (the length of the arrow) and the direction (which way the arrow is pointing).
 The vector \(\underline{a}\) is shown by this arrow. The length of the arrow represents the magnitude of the vector and the direction of the arrow shows the direction of the vector. The vector \(\underline{b}\) is shown by this arrow. The length of the arrow represents the magnitude of the vector and the direction of the arrow shows the direction of the vector. The arrow \(\underline{b}\) is shorter than the arrow \(\underline{a}\) so the vector \(\underline{b}\) has a smaller magnitude than \(\underline{a}\). It can also be seen that vector \(\underline{b}\) has a different direction to vector \(\underline{a}\).
Using a diagram two vector quantities can be added together by drawing the arrows end to end.
 The two vectors can be added by placing the start of one vector at the end of the other. A new vector \(\underline{c}\) is created from the addition of \(\underline{a}\) and \(\underline{b}\). \(\underline{a}+\underline{b}=\underline{c}\) If the vectors are drawn accurately in length using a ruler and in direction using a protractor the length and direction of the new vector can be measured from the diagram. This type of Scale Diagram can be used to find the magnitude and direction of the new vector without calculation.

### References

#### AQA

Vector, pages 143, 157, 162-3, GCSE Physics; Student Book, Collins, AQA
Vector; diagram, page 157, GCSE Physics; Student Book, Collins, AQA
Vectors, pages 114-115, 130-131, GCSE Physics; Third Edition, Oxford University Press, AQA
Vectors, pages 117, 148, GCSE Physics, Hodder, AQA
Vectors, pages 127, 147, GCSE Combined Science Trilogy; Physics, CGP, AQA
Vectors, pages 147, 148, GCSE Physics; The Complete 9-1 Course for AQA, CGP, AQA
Vectors, pages 207, 226, GCSE Combined Science Trilogy 2, Hodder, AQA
Vectors, pages 42, 203, GCSE Combined Science; The Revision Guide, CGP, AQA
Vectors, pages 51, 54, 60, GCSE Physics; The Revision Guide, CGP, AQA
Vectors, pages 83, 224-225, GCSE Biology; Third Edition, Oxford University Press, AQA
Vectors, pages, 46, 48, 99, GCSE Biology; The Revision Guide, CGP, AQA
Vectors; Drawing them, pages 208, GCSE Combined Science Trilogy 2, Hodder, AQA
Vectors; in genetic engineering, page 240, GCSE Combined Science Trilogy; Biology, CGP, AQA
Vectors; in genetic engineering, page 294, GCSE Biology, CGP, AQA
Vectors; momentum as, page 170, GCSE Physics, Hodder, AQA
Vectors; Momentum as, pages 245, 246, GCSE Combined Science Trilogy 2, Hodder, AQA
Vectors; of disease pages 130, 133 ,135, GCSE Biology, CGP, AQA
Vectors; of disease, pages 124, 127, 129, GCSE Combined Science Trilogy; Biology, CGP, AQA
Vectors; representation by arrows, page 119, GCSE Physics, Hodder, AQA

#### Edexcel

Vectors (biology), pages 37, 39, GCSE Combined Science; The Revision Guide, CGP, Edexcel
Vectors (disease transfer), page 105, GCSE Biology, Pearson, Edexcel
Vectors (genetic), page 89, GCSE Biology, Pearson, Edexcel
Vectors, page 12, GCSE Physics; The Revision Guide, CGP, Edexcel
Vectors, pages 22, 205, GCSE Physics, CGP, Edexcel
Vectors, pages 2-3, 132, GCSE Physics, Pearson Edexcel
Vectors, pages 3, 12, 121, GCSE Physics, Pearson Edexcel
Vectors; in disease, page 55, GCSE Biology; The Revision Guide, CGP, Edexcel
Vectors; in disease, pages 154, 156, GCSE Biology, CGP, Edexcel
Vectors; in genetic engineering, page 52, GCSE Biology; The Revision Guide, CGP, Edexcel
Vectors; in genetic engineering, pages 144, 155, GCSE Biology, CGP, Edexcel
Vectors; viruses, page 195, GCSE Biology, Pearson, Edexcel

#### OCR

Vector quantities, page 157, Gateway GCSE Combined Science; The Revision Guide, CGP, OCR
Vectors (genetic engineering), page 204, Gateway GCSE Biology, Oxford, OCR
Vectors, pages 50-51, 65, Gateway GCSE Physics, Oxford, OCR