# Vectors resources

### Facts & Formulae Leaflets (1)

Mathematical Tools for Physical Sciences and Systems Biology

This leaflet is a summary of common mathematical definitions and properties used in the Physical Sciences and Systems Biology contributed to the mathcentre Community Project by Dr Morgiane Richard, University of Aberdeen and reviewed by Mamen Romano and Ian Stansfield, University of Aberdeen.

### iPOD Video (14)

Introduction to vectors - 1

A vector is a quantity that has both a magnitude (or size) and a direction. Both of these properties must be given in order to specify a vector completely. In this unit we describe how to write down vectors, how to add and subtract them, and how to use them in geometry.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Introduction to vectors - 2

A vector is a quantity that has both a magnitude (or size) and a direction. Both of these properties must be given in order to specify a vector completely. In this unit we describe how to write down vectors, how to add and subtract them, and how to use them in geometry.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Introduction to vectors - 3

A vector is a quantity that has both a magnitude (or size) and a direction. Both of these properties must be given in order to specify a vector completely. In this unit we describe how to write down vectors, how to add and subtract them, and how to use them in geometry.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Introduction to vectors - 4

A vector is a quantity that has both a magnitude (or size) and a direction. Both of these properties must be given in order to specify a vector completely. In this unit we describe how to write down vectors, how to add and subtract them, and how to use them in geometry.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Vectors - Scalar Product 1

One of the ways in which two vectors can be combined is known as the scalar product. When we calculate the scalar product of two vectors the result, as the name suggests is a scalar, rather than a vector.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Vectors - Scalar Product 2

One of the ways in which two vectors can be combined is known as the scalar product. When we calculate the scalar product of two vectors the result, as the name suggests is a scalar, rather than a vector.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Vectors - Scalar Product 3

One of the ways in which two vectors can be combined is known as the scalar product. When we calculate the scalar product of two vectors the result, as the name suggests is a scalar, rather than a vector.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Vectors - Scalar Product 4

One of the ways in which two vectors can be combined is known as the scalar product. When we calculate the scalar product of two vectors the result, as the name suggests is a scalar, rather than a vector.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Vectors - Scalar Product 5

One of the ways in which two vectors can be combined is known as the scalar product. When we calculate the scalar product of two vectors the result, as the name suggests is a scalar, rather than a vector.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Vectors - The Vector Product 1

One of the ways in which two vectors can be combined is known as the vector product. When we calculate the vector product of two vectors the result, as the name suggests, is a vector.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Vectors - The Vector Product 2

One of the ways in which two vectors can be combined is known as the vector product. When we calculate the vector product of two vectors the result, as the name suggests, is a vector.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Vectors - The Vector Product 3

One of the ways in which two vectors can be combined is known as the vector product. When we calculate the vector product of two vectors the result, as the name suggests, is a vector.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Vectors - The Vector Product 4

One of the ways in which two vectors can be combined is known as the vector product. When we calculate the vector product of two vectors the result, as the name suggests, is a vector.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Vectors - The Vector Product 5

One of the ways in which two vectors can be combined is known as the vector product. When we calculate the vector product of two vectors the result, as the name suggests, is a vector.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

### Teach Yourself (4)

Cartesian components of vectors

Any vector may be expressed in Cartesian components, by using unit vectors in
the directions of the coordinate axes. In this unit we describe these unit
vectors in two dimensions and in three dimensions, and show how they can be
used in calculations.

Introduction to vectors

A vector is a quantity that has both a magnitude (or size) and a direction.
Both of these properties must be given in order to specify a vector
completely. In this unit we describe how to write down vectors, how to add
and subtract them, and how to use them in geometry.

The scalar product

One of the ways in which two vectors can be combined is known as the scalar product. When we calculate the scalar product of two vectors the result, as the name suggests is a scalar, rather than a vector.

The vector product

One of the ways in which two vectors can be combined is known as the vector product. When we calculate the vector product of two vectors the result, as the name suggests, is a vector.

### Test Yourself (10)

Diagnostic Test - Cartesian components of vectors

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Diagnostic Test - Introduction to Vectors

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Diagnostic Test - Scalar Products

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Diagnostic Test - Vector Products

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Dot and cross product - Numbas

5 questions on vectors. Scalar product, angle between vectors, cross product, when are vectors perpendicular, combinations of vectors defined or not. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.

Exercise - Cartesian components of vectors

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Exercise - Introduction to Vectors

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Exercise - Scalar Products

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Exercise - Vector Products

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Maths EG

Computer-aided assessment of maths, stats and numeracy from GCSE to undergraduate level 2. These resources have been made available under a Creative Common licence by Martin Greenhow and Abdulrahman Kamavi, Brunel University.

### Video (4)

Cartesian components of vectors

Any vector may be expressed in Cartesian components, by using unit vectors in
the directions of the coordinate axes. In this unit we describe these unit
vectors in two dimensions and in three dimensions, and show how they can be
used in calculations. (Mathtutor Video Tutorial).
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Introduction to vectors

A vector is a quantity that has both a magnitude (or size) and a direction.
Both of these properties must be given in order to specify a vector
completely. In this unit we describe how to write down vectors, how to add
and subtract them, and how to use them in geometry. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

The scalar product

One of the ways in which two vectors can be combined is known as the scalar product. When we calculate the scalar product of two vectors the result, as the name suggests is a scalar, rather than a vector. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

The vector product

One of the ways in which two vectors can be combined is known as the vector product. When we calculate the vector product of two vectors the result, as the name suggests, is a vector.
(Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

### Video with captions which require edits (4)

Cartesian components of vectors

Any vector may be expressed in Cartesian components, by using unit vectors in
the directions of the coordinate axes. In this unit we describe these unit
vectors in two dimensions and in three dimensions, and show how they can be
used in calculations. (Mathtutor Video Tutorial).
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Introduction to vectors

A vector is a quantity that has both a magnitude (or size) and a direction.
Both of these properties must be given in order to specify a vector
completely. In this unit we describe how to write down vectors, how to add
and subtract them, and how to use them in geometry. (Mathtutor Video Tutorial)
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

The scalar product

One of the ways in which two vectors can be combined is known as the scalar product. When we calculate the scalar product of two vectors the result, as the name suggests is a scalar, rather than a vector. (Mathtutor Video Tutorial)
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

The vector product

One of the ways in which two vectors can be combined is known as the vector product. When we calculate the vector product of two vectors the result, as the name suggests, is a vector.
(Mathtutor Video Tutorial)
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.