From plane vectors to three-dimensional geometry
Start from the basic operations on plane vectors and extend the dot product and projection to three dimensions. The cross product, normal vectors, and the distance from a point to a plane lead to a GSAT problem on distance in space.
- Work Vector addition and scalar multiplication
The two most basic vector operations: addition and scalar multiplication.
- Work Geometric significance of the dot product
Dot product = projection × length, which brings in angles and projection.
- Explore Spatial vectors, planes, and lines
Up to three dimensions: vectors, planes, and lines in space.
- Work Geometric significance of the cross product
Cross product: the vector product of three-dimensional space.
- Work Plane normal and distance from a point
Normal vectors and the distance from a point to a plane, toward measuring distance in space.
- Exam Skew lines, the common perpendicular, and distance in space
An exam problem to finish: use the whole path on a distance in space.