# Vectors

**AS Level**

- Use vectors in two dimensions
- Calculate the magnitude and direction of a vector and convert between component form and magnitude/direction form
- Add vectors diagrammatically and perform the algebraic operations of vector addition and multiplication by scalars, and understand their geometrical interpretations
- Understand and use position vectors; calculate the distance between two points represented by position vectors
- Use vectors to solve problems in pure mathematics and in context, including forces

**A Level**

- Use vectors in three dimensions
- Use vectors to solve problems in pure mathematics and in context, including kinematics

### Vectors Introduction

This extensive University of Leicester presentation includes a range of vector topics. It aims for students to be able to define what is meant by a vector and differentiate between a vector and scalar quantity, to algebraically manipulate vectors and to calculate the angle between two vectors using the scalar product.

### Vectors *suitable for home teaching*

This collection from Mathcentre contains four resources, introduction to vectors, calculating the vector and scalar products and the Cartesian components of vectors.

Each contains comprehensive notes, examples. and a selection of questions to be completed, for which answers are provided.

### Vectors

This series of interactive excel sheets from The Virtual Textbook provides an introduction to a range of vector topics, from identifying column vectors and finding the magnitude and direction of vectors expressed in column form, to vector geometry topics such as the mid-point of a line, the centroid of a triangle and parallelogram formed by the midpoints of a quadrilateral. The resource alo includes printable worksheets for classroom use.

### Vectors 2

The second vectors resource from The Virtual Textbook shows how vectors can be used to specify journeys and how the vectors** a** and **b** can be used to describe relative position. It also introduces the unit vectors i and j, as well as investigating vectors that define the motion of two objects.

### Vectors

This Odd One Out activity covers a range of mathematical topics, and comes with detailed teachers notes. It asks students to examine the mathematical properties of the three items, promoting discussion to determine which of three numbers or expressions is the odd one out.

It contains two vector questions, the first helps students to explore vector and scalars, the second compares the lines described by three vectors.

### Translation and Vectors

This SMILE resource contain games, investigations, worksheets and practical activities to introduce translations and vector topics. Pack 2 includes activities that ask students to plot journeys using vectors, find the magnitude of a vector, use vector algebra, use vectors to show proof, to add vectors, and divide vectors into a given ratio.

### Triangle Centres

The Carom Maths activity is designed to explore aspects of the subject which may not normally be encountered, to encourage new ways to approach a problem mathematically and to broaden the range of tools that an A Level mathematician can call upon. It uses vectors to help explore the circumcentre, the centroid and the orthocentre of a triangle inscribed within a circle.