Further Work with Vectors

Dive into advanced vector concepts in this comprehensive 6-hour tutorial series. Explore 3D coordinate systems, extend 2D vectors to 3D, and master ratio division with vectors. Learn vector proofs for quadrilaterals and parallelograms, understand 3D dot products and their applications, and practice resolving vectors with projections. Discover vector equations for lines, curves, and spheres in three dimensions. Tackle complex 3D vector problems involving tetrahedrons and parallelogram pyramids. Apply your knowledge to exam-style questions, including line-sphere intersections and 3D parallelograms. Enhance your understanding of vector mathematics through detailed explanations and worked examples.

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).