This course aims to enhance understanding and proficiency in working with vectors in three dimensions. By the end of the course, learners will be able to extend 2D vectors, perform ratio division with vectors, apply 3D dot products, work with vector equations of lines and curves, and solve various 3D vector problems. The course teaches skills such as calculating distances between points, finding angles between vectors, and determining points of intersection. The teaching method includes theoretical explanations, derivations of formulas, worked examples, and application-based problem-solving. This course is intended for individuals interested in advancing their knowledge of vectors, particularly in a three-dimensional space.
Overview
Syllabus
3D Coordinate System (1 of 2: Introduction).
3D Coordinate System (2 of 2: Distance formula).
Extending 2D Vectors (1 of 2: Notation & example).
Extending 2D Vectors (2 of 2: Between two points).
Ratio Division with Vectors (1 of 2: Internal).
Ratio Division with Vectors (2 of 2: External).
Vector Proof: "Unspecial" Quadrilaterals & Parallelograms.
3D Dot Product (1 of 3: Foundational ideas).
3D Dot Product (2 of 3: Deriving the formula for component form).
3D Dot Product (3 of 3: Application to perpendicular vectors).
Applications of Dot Products (1 of 2: Angles between vectors).
Applications of Dot Products (2 of 2: Projections).
Resolving Vectors with Projections (1 of 2: Relation to perpendicular distance).
Resolving Vectors with Projections (2 of 2: Worked example).
Vector Equation of a Line (1 of 2: Lines in 3 dimensions).
Vector Equation of a Line (2 of 2: Worked example).
Applying Vector Equations of Lines (1 of 2: Verifying points on a line).
Applying Vector Equations of Lines (2 of 2: Intercepts & points of intersection).
Vector Equations of Curves (1 of 3: Circle - basic & shifted).
Vector Equations of Curves (2 of 3: Midpoint of a chord).
Vector Equations of Curves (3 of 3: Traversing a circle).
Vector Equations of Spheres (1 of 2: Tangential spheres).
Vector Equations of Spheres (2 of 2: Circle of intersection).
3D Vectors Questions (1 of 2: Tetrahedron).
3D Vectors Questions (2 of 2: Parallelogram pyramid).
Where do a line & sphere intersect? (Exam Question 3 of 10).
Finding vector equation of a 3D line (Exam Question 6 of 10).
Parallelogram in three dimensions (Exam Question 8 of 10).
Taught by
Eddie Woo
