Three-Dimensional Coordinate Systems.

0:00 Three-Dimensional Coordinate Systems.

2:51 Right-Hand Rule.

4:45 XYZ-Coordinate Planes and the regions " Octants".

8:13 Example: Sketch Z = 3 and Y = 5 in R^3.

10:28 Example: Sketch Y = x in R^3.

12:05 The Distance Formula in Three Dimensions.

12:53 Example: Find the distance from the point P (2, -1, 7)

to the point Q (1, -3, 5).

14:26: Equation of a Sphere.

15:04 Example: Show that x^2 + y^2 +z^2 + 4x -6y +2z +6 = 0 is the equation of a sphere and find its center and radius.

18:32 Example: What region in R^3 is represented by the following inequalities? 1 is less than or equal to x^2 + y^2 + z^2 is less than or equal to 4; z is less than or equal to 0.