Master the Fundamentals of Vectors
5.0 (3 ratings)
Course Ratings are calculated from individual students’ ratings and a variety of other signals, like age of rating and reliability, to ensure that they reflect course quality fairly and accurately.
386 students enrolled

Master the Fundamentals of Vectors

Master the fundamentals of vectors
5.0 (3 ratings)
Course Ratings are calculated from individual students’ ratings and a variety of other signals, like age of rating and reliability, to ensure that they reflect course quality fairly and accurately.
386 students enrolled
Last updated 3/2019
English
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Current price: $44.99 Original price: $64.99 Discount: 31% off
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This course includes
  • 4.5 hours on-demand video
  • 1 article
  • 24 downloadable resources
  • Full lifetime access
  • Access on mobile and TV
  • Certificate of Completion
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What you'll learn
  • Basic Vector Operations
  • Scalar (Dot) Product
  • Vector (Cross) Product
  • Three-dimensional Vectors
  • Length of Projection
  • Vector Equations of Straight Lines
  • Equations of Planes
  • Angle between two lines and angle between two planes
  • Shortest Distance from a Point to a Line/Plane
  • Point of Reflection of a Point about a Plane
  • Point of Intersection between a Line and a Plane
  • Intersections between Two/Three Planes
Requirements
  • Basic vector knowledge in elementary mathematics level
  • Able to carry out basic mathematical operations
  • Be proficient in the basic use of a graphic calculator
Description

Dear students,

Welcome to this course "Master the Fundamentals of Vectors"!

This course is designed specially for students who are: doing college-level mathematics, taking their IGCSE/GCE A level, the IB HL Math examinations or simply anyone who is interested to learn the basics of vector .

At the end of the course, and depending on which exams you are taking, you will learn most/all of the following:

  • basic vector operations

  • ratio theorem and midpoint theorem

  • scalar (dot) product

  • length of projection

  • vector (cross) product

  • vector equation of a straight line

  • acute angle between two lines

  • shortest distance from a point to a line

  • equations of a plane (scalar-product, Cartesian, parametric form)

  • distance from a point to a plane

  • point of intersection between a plane and a line

  • point of reflection about a plane

  • acute angle between a plane and a line

  • angle between two planes

  • intersection of two planes

  • intersection of three planes

  • distance between two planes

Along the way, there will be quizzes and practice questions for you to get familiarize with the concepts relating to vectors. There are also several bonus lectures which will further enhance your understanding of the topic. If you encounter any problems, please do not hesitate to contact me for more clarifications.

I hope that you will find this course useful in your academic pursuit. Enjoy the course! Cheers!

Who this course is for:
  • College students who need a good foundation in vector algebra
  • GCE/IGCSE A levels mathematics students
  • IB HL Math students
Course content
Expand all 47 lectures 04:19:54
+ Introduction to Vectors
2 lectures 12:08

Dear student, welcome to the world of vectors! In this course, you will master all the essential concepts of vectors that will prepare you well for tertiary education. Do watch all the videos and attempt the practice questions and quizzes to reap the maximum benefit. Enjoy the course! Cheers! ;-)

Preview 05:32

Please try the practice questions on your own and watch the video to review the answers!

Practice 1 Questions and Answers
06:36
+ Vector Addition and Subtraction
2 lectures 12:19

In this lecture, you will learn about the basic vector operations of addition and subtraction.

Vector Addition and Subtraction
06:00
Practice 2 Questions and Answers
06:19
+ Ratio Theorem
2 lectures 08:00

In this lecture, you will learn a useful vector theorem called the "Ratio Theorem" as well as the "Midpoint Theorem", which is a slight variation from the "Ratio Theorem".

Ratio Theorem
03:05
Practice 3 Questions and Answers
04:55
+ Vector Representations in Cartesian Plane
2 lectures 10:42

In this lecture, you will learn about how to represent vectors in a Cartesian Plane.

Vector Representations in Cartesian Plane
07:10
Practice 4 Questions and Answers
03:32
+ Scalar Product of Vectors
2 lectures 13:44

In this lecture, you will learn about an important vector calculation called the Scalar (or Dot) Product.

Scalar Product of Vectors
11:04
Practice 5 Questions and Answers
02:40
+ Length of Projection
2 lectures 08:54

In this lecture, you will learn about a geometrical calculation of the length of projection.

Length of Projection
04:12
Practice 6 Questions and Answers
04:42
+ Vector(Cross) Product (GCE A levels and IB only)
2 lectures 21:06

In this lecture, you will learn another important vector calculation called the Vector (or Cross) Product.

Vector(Cross) Product (College Level/GCE A levels/IB HL)
14:36
Practice 7 Questions and Answers
06:30
+ Vectors Quiz 1
0 lectures 00:00

There will be 3 questions in this quiz. Please revise the contents learnt from lectures 1 to 14 before attempting the quiz. Good luck! ;-)

Vectors Quiz 1
3 questions
+ Vectors involving Straight Lines
10 lectures 58:39

In this lecture, you will learn how to express the equation of a straight line in vector equation form.

Vector Equation of a Straight Line
09:03
Practice 8 Questions and Answers
04:49

In this lecture, you will learn how to express the vector equation of a line in the Cartesian form.

Preview 04:59
Practice 9 Questions and Answers
04:17

In this lecture, you will learn about the relationships between two lines.

Relationships between Two Lines
09:18

Please try the practice questions on your own and watch the video to review the answers!

Practice 10 Questions and Answers
04:53

In this lecture, you will learn how to calculate the angle between two lines.

Acute Angle between Two Lines
02:56

Please try the practice questions on your own and watch the video to review the answers!

Practice 11 Questions and Answers
03:40

In this lecture, you will learn how to determine the shortest distance from a point to a line.

Shortest Distance from a Point to a Line
07:40

Please try the practice questions on your own and watch the video to review the answers!

Practice 12 Questions and Answers
07:04
+ Vectors involving Planes (for GCE A levels and IB HL)
20 lectures 01:43:16

In this lecture, you will learn about the equation of a vector plane in parametric form.

Equation of a Plane in Parametric Form (College Level/GCE A levels/IB HL)
05:12

Please try the practice questions on your own and watch the video to review the answers!

Practice 13 Questions and Answers
04:06

In this lecture, you will learn about a commonly-used equation format of a plane, called the Scalar-Product form.

Equation of a Plane in Scalar Product Form (for GCE A levels and IB HL)
05:10

Please try the practice questions on your own and watch the video to review the answers!

Practice 14 Questions and Answers
04:27

In this lecture, you will learn how to express the equation of a vector plane in Cartesian form.

Equation of a Plane in Cartesian Form (College Level/GCE A levels/IB HL)
10:43

Please try the practice questions on your own and watch the video to review the answers!

Practice 15 Questions and Answers
03:59

In this lecture, you will learn how to calculate the distance from a point to a plane.

Distance from a Point to a Plane (College Level/GCE A levels/IB HL)
08:49

Please try the practice questions on your own and watch the video to review the answers!

Practice 16 Questions and Answers
06:42

In this lecture, you will be taught how to determine the point of intersection between a plane and a line.

Point of Intersection between a Plane and a Line (College Level/GCE A levels/IB
04:23

Please try the practice questions on your own and watch the video to review the answers!

Practice 17 Questions and Answers
04:32

In this lecture, you will learn how to determine the coordinates and position vector of the foot of perpendicular from a point to a plane.

Foot of Perpendicular from a Point to a Plane (College Level/GCE A levels/IB HL)
05:39

Please try the practice questions on your own and watch the video to review the answers!

Practice 18 Questions and Answers
05:38

In this lecture, you will learn about how to calculate the acute angle between a plane and a line.

Acute Angle between a Plane and a Line (College Level/GCE A levels/IB HL)
03:16

Please try the practice questions on your own and watch the video to review the answers!

Practice 19 Questions and Answers
04:11

In this lecture, you will learn how to calculate the angle between two planes.

Angle between Two Planes (College Level/GCE A levels/IB HL)
03:30

Please try the practice questions on your own and watch the video to review the answers!

Practice 20 Questions and Answers
04:04

In this lecture, you will learn how to determine the equation of the line of intersection between two planes.

Intersection of Two Planes (College Level/GCE A levels/IB HL)
03:55

Please try the practice questions on your own and watch the video to review the answers!

Practice 21 Questions and Answers
05:42

In this lecture, you will learn about the possible intersections between three planes.

Intersection of Three Planes (College Level and IB HL)
04:04

Please try the practice questions on your own and watch the video to review the answers!

Practice 22 Questions and Answers
05:14