Problems: Lines, Surfaces, and Vector Functions in Three-Dimensional Coordinate System

In this chapter, the basic and advanced problems of lines, surfaces, vector functions, and parametric vector functions in three-dimensional coordinate systems are presented. The subjects include polar coordinate system, cartesian coordinate system, equation of surface, surface type, surface area, definite vector integral, indefinite vector integral, unit tangent vector, unit normal vector, general equation of different surfaces such as cylinder, ellipsoid, one-sheet hyperboloid, two-sheet hyperboloid, cone, elliptic paraboloid, and hyperbolic paraboloid, circular curve, curve type, and amount of curvature of a curve. In this chapter, the problems are categorized in different levels based on their difficulty levels (easy, normal, and hard) and calculation amounts (small, normal, and large). Additionally, the problems are ordered from the easiest problem with the smallest computations to the most difficult problems with the largest calculations.