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.