Introduction to Vectors

Name: Introduction to Vectors
Rating: 5.0 (1 reviews)

Definition, properties, and applications of Vectors

Created byTaman Belajar, Bina Nusantara University

Last updated 8/2025

English

What you'll learn

Understand the definition and geometric representation of vectors
Learn about vector operations, including addition, dot product, and cross product.
Understand vector components and their applications in real-world scenarios.
Apply vector concepts to solve problems in engineering, physics, and computer graphics.

Course content

3 sections • 11 lectures • 46m total length

Overview1:52
Discover the fundamentals of vectors and perform vector operations. Apply norm, distance, and orthogonal projection in Cartesian and n-space, including dot product, cross product, and parametric equations.
What is Vector?1:32
Define a vector as an arrow representing direction and magnitude, with equal vectors sharing the same length and direction, denoted by its initial point and terminal point.
Vector Operations: Geometric Definition4:58
Learn vector operations defined geometrically, including addition via parallelogram and triangle rules, subtracting using minus v, and scalar multiplication by k in two- or three-space.
Vectors in Coordinate Systems3:58
Define vectors in two- and three-dimensional coordinate systems and determine their components from initial and terminal points using x2−x1, y2−y1, and z2−z1.
Vector in 2-Space, 3-Space, and n-Space

Vector Operations: n-Space Definition5:26
Define real n-space and ordered n-tuples, establish vector equality by component, and perform vector operations such as addition, scalar multiplication, negation, and subtraction with concrete examples.
Norm and Distance in n-Space4:16
Explore the norm of a vector in n-space as the square root of the sum of squares, and measure the distance between vectors as the norm of their difference.
Dot Product4:30
Learn to compute the dot product as the euclidean inner product in rn, where u dot v equals the sum of ui vi for orthogonality testing.
Vector Algebra

Orthogonal Projections4:52
Learn to decompose a vector into a projection along a and a component orthogonal to a, and compute it with the formula (u·a)/(||a||^2) a, plus the orthogonal remainder.
Norm of a Projection3:46
Learn the norm of the orthogonal projection of u onto A. Use the formulas ||proj_A(u)|| = |u·A|/||A|| or ||u|| cos theta, with a concrete example u=(2,-1,3), A=(4,-1,2).
Vector and Parametric Equations of Lines and Planes5:08
Learn to express lines and planes with parametric equations, using x = x0 + t v for lines and x = x0 + t1 v1 + t2 v2 for planes.
Cross Product6:00
Compute the cross product of three-dimensional vectors using determinant notation, and relate its norm to |u||v| sin θ, illustrating parallelogram and triangle areas.
Orthogonal Vectors and Cross Product

Requirements

No requirement needed

Description

Course 'Introduction to Vectors' provides a comprehensive introduction to vectors, focusing on their definition, properties, and applications. The course aims to build a strong foundational understanding of vectors and their operations. By the end of the course, students will be able to understand and apply vector concepts in two, three, and n-dimensional spaces.

Course Objectives:

Understand the definition and geometric representation of vectors.
Learn about vector operations, including addition, dot product, and cross product.
Understand vector components and their applications in real-world scenarios.
Apply vector concepts to solve problems in engineering, physics, and computer graphics.

The modules that will be discussed include:

What is Vector?
Vector Operations: Geometric Definition
Vectors in Coordinate Systems
Vector Operations: n-Space Definition
Norm and Distance in n-Space
Dot Product
Orthogonal Projections
Norm of a Projection
Vector and Parametric Equations of Lines and Planes
Cross Product

Course Content:

Videos: Each module includes video lectures that explain theoretical concepts and their applications.
Lecture Notes: Detailed notes for each module, providing in-depth explanations and examples.
Quizzes: Interactive quizzes at the end of each module to test understanding and reinforce learning.

This course is ideal for students looking to gain practical knowledge of vectors and their use in various scientific and engineering problems.

Who this course is for:

This course is ideal for students looking to gain practical knowledge of vectors and their use in various scientific and engineering problems

Introduction to Vectors

What you'll learn

Explore related topics

Course content

Vector in 2-Space, 3-Space, and n-Space4 lectures • 12min

Vector Algebra3 lectures • 14min

Orthogonal Vectors and Cross Product4 lectures • 20min

Requirements

Description

Who this course is for: