Further vectors
Section overview:
The PowerPoint below provides an overview of material in this topic, including explanations and examples - for the full experience, open in a new tab then download it. All exercise references are to the new specification Pearson textbook - you can access the digital version for free or buy your own for extra practice.
Written summary notes are also given below for quick revision of key points, plus a selection of exam-style questions (with solutions) to test your understanding.
CP1-Chp9-Vectors.pptx
Explore further: Learn how maths is used at Pixar
There's a whole online course on the topic here!
Notes:
Section 1 Notes - Scalar (dot) product
Section 2 Notes - Lines: equations, angles and intersections
Section 3 Notes - Planes: equations, angles and intersections
Section 4 Notes - Distances
Summary questions:
Extra resources:
Use the videos below to support your understanding of the topic. The ones on the left are specific to the course, building up to demos of exam-style questions; the ones on the right are for your own amusement, although the alternative outlook may provide you with a deeper overall understanding and appreciation of the topic.
Topic videos:
- Using vectors (Nearer Maths recap - inc Y13)
- The scalar (dot) product of two vectors
- The angle between two vectors
- The vector equation of a line in 2D
- The vector equation of a line in 3D
- The equation of a line in 3D in Cartesian form
- The intersection of lines in 2D
- The intersection of lines in 3D
- The equation of a plane in parametric form
- The equation of a plane using the normal to the plane
- The equation of a plane in Cartesian form
- The angle between two planes
- The intersection of a line and a plane
- The angle between a line and a plane
- The perpendicular distance from a point to a line [Dot product and calculus methods]
- The perpendicular distance from a point to a plane [Formulae booklet]
- The perpendicular distance between two parallel lines [Dot product method shown; calculus method is also valid]
- The perpendicular distance between skew lines [This video demonstrates the dot product method only]
In the new specification, you are not required to be able to calculate or apply the vector (cross) product. However, you are given the information for it in the formulae booklet (or you can find it on the calculator), plus it is often a more efficient method!
Cross product videos:
- Introduction and definitions
- Finding equations of planes using the vector (cross) product
- Shortest distance between skew lines (cross product method) - Intro
- Shortest distance between skew lines (cross product method) - Example
Extra fun! An additional playlist outlining some of the deeper underlying principles of vectors and matrices.