Master the Fundamentals of Vectors

Name: Master the Fundamentals of Vectors
Rating: 4.6 (7 reviews)

Master the fundamentals of vectors

Created byDr Ling Meng Kay Daniel, PhD

Last updated 3/2019

English

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

Course content

12 sections • 47 lectures • 4h 19m total length

Introduction to Vectors5:32
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! ;-)
Practice 1 Questions and Answers6:36
Please try the practice questions on your own and watch the video to review the answers!

Vector Equation of a Straight Line9:03
In this lecture, you will learn how to express the equation of a straight line in vector equation form.
Practice 8 Questions and Answers4:49
Cartesian Equation of a Straight Line4:59
In this lecture, you will learn how to express the vector equation of a line in the Cartesian form.
Practice 9 Questions and Answers4:17
Relationships between Two Lines9:18
In this lecture, you will learn about the relationships between two lines.
Practice 10 Questions and Answers4:53
Please try the practice questions on your own and watch the video to review the answers!
Acute Angle between Two Lines2:56
In this lecture, you will learn how to calculate the angle between two lines.
Practice 11 Questions and Answers3:40
Please try the practice questions on your own and watch the video to review the answers!
Shortest Distance from a Point to a Line7:40
In this lecture, you will learn how to determine the shortest distance from a point to a line.
Practice 12 Questions and Answers7:04
Please try the practice questions on your own and watch the video to review the answers!

Equation of a Plane in Parametric Form (College Level/GCE A levels/IB HL)5:12
In this lecture, you will learn about the equation of a vector plane in parametric form.
Practice 13 Questions and Answers4:06
Please try the practice questions on your own and watch the video to review the answers!
Equation of a Plane in Scalar Product Form (for GCE A levels and IB HL)5:10
In this lecture, you will learn about a commonly-used equation format of a plane, called the Scalar-Product form.
Practice 14 Questions and Answers4:27
Please try the practice questions on your own and watch the video to review the answers!
Equation of a Plane in Cartesian Form (College Level/GCE A levels/IB HL)10:43
In this lecture, you will learn how to express the equation of a vector plane in Cartesian form.
Practice 15 Questions and Answers3:59
Please try the practice questions on your own and watch the video to review the answers!
Distance from a Point to a Plane (College Level/GCE A levels/IB HL)8:49
In this lecture, you will learn how to calculate the distance from a point to a plane.
Practice 16 Questions and Answers6:42
Please try the practice questions on your own and watch the video to review the answers!
Point of Intersection between a Plane and a Line (College Level/GCE A levels/IB4:23
In this lecture, you will be taught how to determine the point of intersection between a plane and a line.
Practice 17 Questions and Answers4:32
Please try the practice questions on your own and watch the video to review the answers!
Foot of Perpendicular from a Point to a Plane (College Level/GCE A levels/IB HL)5:39
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.
Practice 18 Questions and Answers5:38
Please try the practice questions on your own and watch the video to review the answers!
Acute Angle between a Plane and a Line (College Level/GCE A levels/IB HL)3:16
In this lecture, you will learn about how to calculate the acute angle between a plane and a line.
Practice 19 Questions and Answers4:11
Please try the practice questions on your own and watch the video to review the answers!
Angle between Two Planes (College Level/GCE A levels/IB HL)3:30
In this lecture, you will learn how to calculate the angle between two planes.
Practice 20 Questions and Answers4:04
Please try the practice questions on your own and watch the video to review the answers!
Intersection of Two Planes (College Level/GCE A levels/IB HL)3:55
In this lecture, you will learn how to determine the equation of the line of intersection between two planes.
Practice 21 Questions and Answers5:42
Please try the practice questions on your own and watch the video to review the answers!
Intersection of Three Planes (College Level and IB HL)4:04
In this lecture, you will learn about the possible intersections between three planes.
Practice 22 Questions and Answers5:14
Please try the practice questions on your own and watch the video to review the answers!

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 familiarized 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!

Dr Ling, PhD

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

Master the Fundamentals of Vectors

What you'll learn

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Course content

Introduction to Vectors2 lectures • 12min

Vector Addition and Subtraction2 lectures • 12min

Ratio Theorem2 lectures • 8min

Vector Representations in Cartesian Plane2 lectures • 11min

Scalar Product of Vectors2 lectures • 14min

Length of Projection2 lectures • 9min

Vector(Cross) Product (GCE A levels and IB only)2 lectures • 21min

Vectors Quiz 10

Vectors involving Straight Lines10 lectures • 59min

Vectors involving Planes (for GCE A levels and IB HL)20 lectures • 1hr 43min

Requirements

Description

Who this course is for: