# Master the Fundamentals of Vectors

Master the fundamentals of vectors

Dear students,

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

• Introduction to Vectors –> 2 lectures • 12min.
• Vector Addition and Subtraction –> 2 lectures • 12min.
• Ratio Theorem –> 2 lectures • 8min.
• Vector Representations in Cartesian Plane –> 2 lectures • 11min.
• Scalar Product of Vectors –> 2 lectures • 14min.
• Length of Projection –> 2 lectures • 9min.
• Vector(Cross) Product (GCE A levels and IB only) –> 2 lectures • 21min.
• Vectors Quiz 1 –> 0 lectures • 0min.
• Vectors involving Straight Lines –> 10 lectures • 59min.
• Vectors involving Planes (for GCE A levels and IB HL) –> 20 lectures • 1hr 43min.
• Vectors Quiz 2 –> 0 lectures • 0min.
• Summary and Conclusions –> 3 lectures • 11min.

Requirements

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

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