M408M Learning Module Pages
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Chapter 10: Parametric Equations and Polar Coordinates

Chapter 12: Vectors and the Geometry of Space

Learning module LM 12.1: 3-dimensional rectangular coordinates:

Learning module LM 12.2: Vectors:

Learning module LM 12.3: Dot products:

Learning module LM 12.4: Cross products:

Learning module LM 12.5: Equations of Lines and Planes:

Learning module LM 12.6: Surfaces:

       Surfaces and traces
      Level curves
      Level surfaces
      Worked problems

Chapter 13: Vector Functions

Chapter 14: Partial Derivatives

Chapter 15: Multiple Integrals

Worked problems

Worked problems

In this video we work three problems about quadric surfaces:

  • Put the equation $\displaystyle{4x^2+y^2+4z^2-4y-24z+36=0}$ in standard form, and identify the surface.
  • Find the equation of the surface consisting of all points equidistant from $(-1,0,0)$ and the plane $x=1$.
  • Use traces to identify the surface $9x^2-y^2+z^2=1$.