APEX Calculus - Vectors

Explore the fundamentals of vectors and their applications in three-dimensional space through this comprehensive 7-hour course. Begin with an introduction to Cartesian coordinates in 3D, learning to calculate distances, lengths of line segments, and equations of spheres, planes, and cylinders. Delve into vector operations, including addition, subtraction, and scalar multiplication, before mastering dot products and cross products. Apply these concepts to real-world scenarios such as work calculations and geometric problems. Investigate lines and planes in 3D space, learning to determine their equations, intersections, and distances. Gain practical skills in solving complex spatial problems and understanding the mathematical foundations of 3D geometry.

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.