Explore equations of lines and planes in three-dimensional space in this comprehensive lecture on linear algebra. Begin with a review of lines in 2D, including their Cartesian and parametric equations, before delving into the novel concept of representing all 2D lines as a Möbius band. Progress to 3D geometry, examining both lines and planes using determinants rather than inner or cross products. Learn to find intersections, solve systems of equations, and convert between parametric and Cartesian forms for both lines and planes. Gain insights into special cases, pencils and stacks of lines, and unique methods for finding meets of planes rarely covered in traditional texts. This in-depth exploration provides a solid foundation for understanding the geometry of lines and planes in 3D space.