4 - Vectors

An introduction of the use of vectors in two and three dimensions. Learn about: magnitude of a vector, algebraic operations of vector addition and multiplication by scalars, and their geometrical interpretations, position vectors, the distance between two points, vector equations of lines, the scalar product and the vector product.

Types of vectors

Unit vectors

Vector addition

a-b and b-a

Vector subtraction

Multiplication by a scalar

Magnitude

Equations of lines

O-test 1

O-test 3

Randomised Exam Q 2008

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Example 8

O-test

Magnitude 4

2D add and subtract

Distance between two points

Intersection with a circle

2D add and subtract 2

3D add and subtract

Multiplication by a scalar 2

Unit vectors

Unit vectors 2

Unit vectors 3

Equations of lines

Equations of lines 2

Equations of lines 3

Equations of lines 4

Equations of lines 5

Intersecting lines

Area of a triangle

Area of a triangle 2

Vector to cartesian form

Scalar product

Angle between vectors

Angle between vectors 2

Angle between 2D lines

Angle between 2D lines 2

Angle between 3D lines

Foot of perpendicular

Perpendicular vectors

Perpendicular vectors 2

Perpendicular vectors 3

Perpendicular vectors 4

Perpendicular lines

Perpendicular lines 2

Collinear points

Memorise the formulae

Diagonals of a parallelogram

Extended problem 1

Extended problem 2

Sequence O-test

O-test 1

O-test 2

O-test 3

O-test 4

O-test 5

O-test 6

O-test 7

O-test 8

Exam O-test 1

Exam O-test 2

Exam O-test 3

Exam O-test 4

Exam O-test 5

Exam timed O-test

Randomised Exam Q 2000

Randomised Exam Q 2000

Randomised Exam Q 2000

Randomised Exam Q 2002

Randomised Exam Q 2003

Randomised Exam Q 2003

Randomised Exam Q 2004

Randomised Exam Q 2005

Randomised Exam Q 2005

Randomised Exam Q 2006

Randomised Exam Q 2006

Randomised Exam Q 2006

Randomised Exam Q 2006

Randomised Exam Q 2007

Randomised Exam Q 2007

Randomised Exam Q 2007

Randomised Exam Q 2007

Randomised Exam Q 2008

Randomised Exam Q 2008

Randomised Exam Q 2008

Randomised Exam Q 2008

Randomised Exam Q 2008

Randomised Exam Q 2008

Randomised Exam Q 2008

Randomised Exam Q 2008

Randomised Exam Q 2008

Randomised Exam Q 2008

Randomised Exam Q 2008

Randomised Exam Q 2009

Randomised Exam Q 2009

Randomised Exam Q 2009

Randomised Exam Q 2009

Randomised Exam Q 2009

Randomised Exam Q 2009

Randomised Exam Q 2010

Randomised Exam Q 2011

Randomised Exam Q 2014

Visualising 3D vectors

Planes 1

Planes 2

Planes 3

Coordinates 1

Coordinates 2

Coordinates 3

3D Vectors

Distance

Distance 2

Pyramid

Prism

Observation O-test

O-test 1

Circle theorem

The cosine rule

The orthocentre

Tetrahedron

Parallelogram

Rhombus

Pythagoras

Definition

Illustration

Perpendicular unit vectors

Properties

Properties 2

Properties 3

Angle between two vectors

Area of triangle

Area of parallelogram

O-test 1

O-test 2

O-test 3

Randomised Exam Q 2008

Visualizing

Visualizing 2

Visualizing 3

Equation of a plane

Equation of a plane 2

Vector equation of a plane

Equation of a plane 3

Vector equation of a plane 2

Perpendiculars to planes

Angle between planes

Perpendicular distance

Line of intersection

Point of intersection

Point of intersection 2

Line in plane

O-test 1

O-test 2

O-test 3

Exam O-test

Randomised Exam Q 2005

Randomised Exam Q 2007

Randomised Exam Q 2008

Randomised Exam Q 2008

Randomised Exam Q 2008

Randomised Exam Q 2008

Randomised Exam Q 2008

Randomised Exam Q 2008

Randomised Exam Q 2008

Randomised Exam Q 2009

Tractor

A pleasure boat

Two boats

Two people

Two submarines

O-test 1

O-test 9

Mindmap

Formulae