This course introduces vectors and their geometric applications in three-dimensional space. It covers vector operations, dot and cross products, coordinates, lines, planes, distances, and common surfaces.

Syllabus

Vectors: Space Coordinates - 01. Cartesian coordinates in 3D.
Vectors: Space Coordinates - 02. Distance.
Vectors: Space Coordinates - 03. Length of a line segment.
Vectors: Space Coordinates - 04. Spheres.
Vectors: Space Coordinates - 05. Example: Sphere.
Vectors: Space Coordinates - 06. Planes.
Vectors: Space Coordinates - 07. Example: Planes.
Vectors: Space Coordinates - 08. Cylinders.
Vectors: Space Coordinates - 09. Example: Cylinders.
Vectors: Space Coordinates - 10. Surfaces of Revolution.
Vectors: Space Coordinates - 11. Example: Surfaces of Revolution.
Vectors: Space Coordinates - 12. Quadric Surfaces.
Vectors: Space Coordinates - 13. Example: Quadric Surfaces.
Vectors: Introduction - 01. Introduction.
Vectors: Introduction - 02. Example: Sketch.
Vectors: Introduction - 03. Algebraic Addition.
Vectors: Introduction - 04. Algebraic Scalar Multiplication.
Vectors: Introduction - 05. Example: Addition.
Vectors: Introduction - 06. Example: Subtraction.
Vectors: Introduction - 07. Example: Scalar Multiplication.
Vectors: Introduction - 08. Scalar Multiplication and Magnitude.
Vectors: Introduction - 09. Unit Vectors.
Vectors: Introduction - 10. Example: Unit Vectors.
Vectors: Introduction - 11. Parallel Vectors.
Vectors: Introduction - 12. Example: Weight hanging from two chains.
Vectors: Dot Products - 01. Introduction.
Vectors: Dot Products - 02. Example.
Vectors: Dot Products - 03. Properties.
Vectors: Dot Products - 04. Geometric Formula.
Vectors: Dot Products - 05. Example: Angles.
Vectors: Dot Products - 06. Orthogonality.
Vectors: Dot Products - 07. Orthogonal Projection.
Vectors: Dot Products - 08. Example: Projection.
Vectors: Dot Products - 09. Orthogonal Decomposition.
Vectors: Dot Products - 10. Work.
Vectors: Cross Products - 01. Introduction.
Vectors: Cross Products - 02. Example.
Vectors: Cross Products - 03. Determinant Formula.
Vectors: Cross Products - 04. Example.
Vectors: Cross Products - 05. Properties.
Vectors: Cross Products - 06. Angles.
Vectors: Cross Products - 07. Application: Area of a Parallelogram.
Vectors: Cross Products - 08. Application: Area of a Triangle.
Vectors: Cross Products - 09. Application: Volume of a Parallelepiped.
Vectors: Lines - 01. Introduction.
Vectors: Lines - 02. Example.
Vectors: Lines - 03. Example.
Vectors: Lines - 04. Comparing lines.
Vectors: Lines - 05. Distance from a Point to a Line.
Vectors: Lines - 06. Example: Distance (point to line).
Vectors: Lines - 07. Distance Between Skew Lines.
Vectors: Lines - 08. Example: Distance (Between Skew Lines).
Vectors: Planes - 01. Introduction.
Vectors: Planes - 02. Example: Plane Through 3 Points.
Vectors: Planes - 03. Example: Plane Orthogonal to Line.
Vectors: Planes - 04. Example: Intersection of two Planes.
Vectors: Planes - 05. Example: Intersection of two planes (algebraic solution).
Vectors: Planes - 06. Example: Intersection of a Line and Plane.
Vectors: Planes - 07. Distance.
Vectors: Planes - 08. Example: Distance.