# Vectors and Scalars

- the distinction between vector and scalar quantities
- resolution of vectors into two components at right angles
- addition rule for two vectors
- calculations for two perpendicular vectors

Those students who studied separate sciences at GCSE are likely to have encountered the concept of vectors before, while those who studied dual award will need a little more support.

It is important the students are aware of the differences between vector and scalar properties; that being that vectors have a direction. Once they can identify which quantities are which they need to be able to resolve vectors into their two components at right angles, add them and then move on to more complicated calculations involving perpendicular vectors.

Some students, naturally, will struggle with the maths of this, and some may also find visualising this concept difficult. There is some work that can be done to help visualise, including making arrows to represent vectors and arranging these appropriately.

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## Links and Resources

### Episode 201: Scalars and Vectors

A suggested teaching order which is part of the 'Teaching Advanced Physics' scheme from Institute of Physics.

It gives a clear overview of the topic, including teacher notes, student notes, worked examples and practice questions, and will prove invaluable to those new to teaching A level physics.

Teachers new to teaching A level physics will appreciate the practical advice on the last page

### Vectors *suitable for home teaching*

These resources are provided by Mathcentre . Some of the topics covered include an introduction to vectors and the cartesian components of vectors.

Comprehensive notes, with clear descriptions, for each resource are provided, together with relevant diagrams and examples. Each pdf contains worked examples as well as practice questions. The 'Key points' section in the notes provide a useful summary of the ideas presented.

Written from a maths point of view, the first (Introduction to vectors) and last (Cartesian components of vectors) sections of this resource will be useful to a physics teacher to see how vectors are taught and notated in maths lessons and could be used to help plan lessons, as well as to consolidate subject knowledge where necessary.

### Vectors Introduction

This interactive resource, produced by the University of Leicester, is designed to enable students to explore vectors, beginning with the definition of a vector followed by the algebra of vectors and the scalar product.

This would make a great introductory lesson to the topic, particularly with the interactive parts of the presentation, although some editing may be required to make it appropriate for your course/students.

In order to access the interactive parts it is necessary to 'enable editing' and then 'enable content'. The presentation is 41 slides long, the first 31 are probably the most useful for A level physics. This is another maths focussed resource, so be aware of differences in notation between the two subjects.

The opening slides of the presentation explain the difference between scalar and vector quantities followed by a simple activity.

The first presentation explains the properties of vectors including line vectors, free vectors, the modulus of a vector, equal vectors, negative vectors, multiplying a vector by a scalar quantity, unit vectors and the angle between two vectors.

The second presentation explains Cartesian vectors, introducing i, j and k unit vectors followed by an interactive page looking at different vector notation in two dimensions.

The algebra of vectors covers the addition of vectors, multiplication by a scalar and the magnitude of a vector.

### Vectors

A series of videos from the Khan Academy, starting with an introduction to vectors and including addition of vectors

This is a lovely interactive resource, which could be set as classwork or homework to encourage independent work from students. After each video there is a link to 'practice this concept' which leads students to a series of questions. These questions contain a series of hints and worked examples to enable students who are struggling to reach the correct answer. If you use it in class, you will need a stable internet connection and to check that Youtube is not blocked in your school. Each student will need a pair of headphones as well.

There is also a questions section to go with each video where the students can 'ask the expert' in order to clarify their ideas. Should they choose to register with the site it keeps track of the progress that they make in the 'practice this concept' section.

It would work well where a student has missed a lesson to help them catch up work.

### Physics Classroom - Resolution of Vectors

These are notes on how to resolve vectors into two components at right angles.

This is best used as either something to help teachers plan a series of lessons around the subject, or set as homework for the students to read, take notes and support learning that they have done in class.

Subject(s) | Science |
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Tags | n.a |

Age | 16-19 |

Last updated | 12 July 2016 |

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URL | https://www.stem.org.uk/lxpab |