**12.1 - 3D Coordinates**

Example 3 - Distance between two coordinates

Example 4 - Parabola with z=3

Example 7 - 3D inequalities and systems

Example 8 - Volume inside cube but outside sphere

Example 1 - Equal vectors from separate starting points

Example 3 - Angle between two vectors

Example 5 - Direction cosines and direction angles

Example 5 - Scalar triple product and the volume of a parallelepiped

**12.5 - Equations of 3D Lines and Planes**

Example 1 - 3D line based on direction vector and starting point

Example 7 - Line of intersection between planes and the angle between planes

Example Overload! All quadric surface examples from lecture in one.

**13.1 - Vector Functions and Space Curves**

Example 4 - Space curve of intersection between surfaces

Example 6 - Motion of Charged Particle in Electric/Magnetic Field

**13.2 - Calculus of Space Curves**

Example 2 - Tangent line to a space curve

**13.3 - Arc Length and Curvature**

Example 1,2,4,6,7 - Helix space curve, TNB frame, Osculating Plane, etc.

**13.4 - Motion in Space - Velocity and Acceleration**

Just For Fun - Home Run or Not? Adjust Initial Velocity and Elevation Angle

**14.1 - Functions in Several Variables**

Example 5 - Comparing Graph in R^3 to Contour Map on R^2

**14.3 - Partial Derivatives**

Example 8/9 - Solutions to Laplace's equation and the Wave equation.

**14.4 - Tangent Planes and Linear Approximations**

Example 2 - Tangent plane to the elliptic paraboloid

**14.6 - Directional Derivatives**

Example 2 - Graph of the tangent plane and tangent lines given by the partial derivatives and directional derivatives.

**14.7 - Minimum and Maximum Values**

Examples 1-4: Second Derivative Test

**15.1 - Double Integrals over Rectangles**

Example 2 - Using Iterated Integrals to calculate volume

Example 4 - Using Triple Integral to calculate volume

**15.7 - Triple Integrals in Cylindrical Coordinates**

Example 2 - Using triple integral to calculate volume

*Example 1 - Gravitational Field, A Conservative Vector Field*

**16.2 - Line Integrals**

*Example 1 - Evaluating a Line Integral*

**16.6 - Parametric Surfaces and Their Areas**

*Example 2 - Graph Parametric Surfaces in GeoGebra*

**16.6 - Parametric Surfaces and Their Areas**

*Example 6 - Tangent Plane to Paraboloid*

*Example 1 - Evaluating a line integral using a surface integral*