Calculus: Analytic Geometry and Calculus, with Vectors

46 Analytic geometry in two dimensions The physical significance of the constants in (1.671), (1.672), and (1.673) is worthy of ...

1.6 Introduction to velocity and acceleration 47 toward the center. The length of the vector r is always R, and the length of th ...

2 Vectors and geometry in three dimensions 2.1 Vectors in E3 To facilitate discussions and solutions of problems in geometry and ...

2.1 Vectors in E, 49 first point to the second point as in Figure 2.111. The purpose of the arrowhead is to show that the vector ...

50 Vectors and geometry in three dimensions The sum r of two vectors u and v is,*s-in-Figttre-2-4-3, the vector which runs from ...

2.1 Vectors in E, 51 is called the angle between u and v or the angle which u makes with v or the angle which v makes with u. Th ...

52 Vectors and geometry in three dimensions of the projection of V on u. In case -Ir/2 < 0 < in, the scalar product is the ...

2.1 Vectors in E, 53 Problems 2.19 1 As in Figure 2.191, let A, B, C, , H be equally spaced points on the line P1P2 with C = PI ...

54 Vectors and geometry in three dimensions P3 P2 6 We are going to prove a theorem in geome- try. As in Figure 2.194, let P1, P ...

2.1 Vectors in E, 55 10 Prove that if Pi, P2, P,, P4 are the vertices of a square having its center at C, then OC =OPi -I- OP2 + ...

S6 Vectors and geometry in three dimensions 17 Sketch a figure showing four points 0, P1i P2, and Q in Es and suppose that IOQI ...

2.1 Vectors in Ea 57 interval 0 < 0 < a, is (as in trigonometry) an angle which the line from 0 to P makes with the positi ...

58 Vectors and geometry in three dimensions 22 Using the definition of Problem 21, prove that if (1) Clvl + C2v2 + C3v3 = 0, whe ...

2.2 Coordinate systems and vectors in E3 59 n exceeds 3, the simplex does not have a plebeian name; it is an n-dimensional simpl ...

60 Vectors and geometry in three dimensions at the origin. The intersection (or section) of the sphere and the yz plane is a cir ...

2.2 Coordinate systems and vectors in E, 61 As in Figure 2.242, let OP be the vector running from the origin 0 to the point P(x, ...

62 Vectors and geometry in three dimensions for the length of the vector P1P2, that is, for the distance between P1 and P2. This ...

2.2 Coordinate systems and vectors in E3 63 The final figure should look much like Figure 2.21. It seems that we do not inherit ...

64 Vectors and geometry in three dimensions 11 Make a sketch showing an x, y, z coordinate system,the sphere S having the equati ...

2.2 Coordinate systems and vectors in Es 65 which make the angle a with L. Supposing that 0 < a < a/2, sketch the cir- cul ...