Mr. Integral

THE BIG IDEA

Vectors and Geometry in Space

How do we describe direction and motion in space?

Vectors attach direction to magnitude. Their products distinguish alignment from perpendicular area, and vector-valued curves let calculus follow a path through three dimensions.

Begin the first lesson →See the lesson route ↓

4 lessons · No deadlines or locked lessons

SEE THE CONNECTIONS

How the ideas fit together.

A map of the main ideas. Follow a node to its lesson.

  1. Start with01Vector products
  2. directions and normals describe02Lines & planes
  3. letting position vary gives03Motion
  4. tracking the turn reveals04Curvature

YOUR LEARNING ROUTE

One idea at a time.

Read the explanation, use the visualization, then try the check before opening its reasoning.

Keep the unit cheat sheet handy →
Lessons in this unit4 lessons
  1. 01Vectors, Dot Products and Cross ProductsChoose a dot or cross product from the scalar or directional quantity being modeled.
  2. 02Lines and Planes in SpaceUse direction and normal vectors to describe incidence, intersection and distance.
  3. 03Space Curves, Velocity and AccelerationDifferentiate a vector trajectory and distinguish speed, velocity and distance traveled.
  4. 04Arc Length, Curvature and TurningSeparate a path’s geometry from the speed at which it is traversed.