Practice Exercises in .NET
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7 Solve the system of equations from the solution to Problem 5, verifying the polar coordinates of points P and Q in Fig 38 8 Based on the information given in Problem 5, what are the Cartesian xycoordinate equations of line L and circle C in Fig 38 9 Solve the system of equations from the solution to Problem 8 to determine the Cartesian coordinates of the intersection points P and Q in Fig 38 10 Based on the polar coordinates of points P and Q in Fig 38 (the solutions to Problems 6 and 7), use the conversion formulas to derive the Cartesian coordinates of those two points CHAPTER
Vector Basics
We can define the length of a line segment that connects two points, but the direction is ambiguous If we want to take the direction into account, we must make a line segment into a vector Mathematicians write vector names as bold letters of the alphabet Alternatively, a vector name can be denoted as a letter with a line or arrow over it The Cartesian Way
In diagrams and graphs, a vector is drawn as a directed line segment whose direction is portrayed by putting an arrow at one end When working in twospace, we can describe vectors in Cartesian coordinates or in polar coordinates Let s look at the Cartesian way first Endpoints, locations, and notations Figure 41 shows four vectors drawn on a Cartesian coordinate grid Each vector has a beginning (the originating point) and an end space (the terminating point) In this situation, any of the four vectors can be defined according to two independent quantities: The length (magnitude) The way it points (direction) It doesn t matter where the originating or terminating points actually are The important thing is how the two points are located with respect to each other Once a vector has been defined as having a specific magnitude and direction, we can slide it around all over the coordinate plane without changing its essential nature We can always think of the originating point for a vector as being located at the coordinate origin (0,0) When we place a vector so that its originating point is at (0,0), we say that the vector is in standard form The standard form is convenient in Cartesian

