in gaining familiarity with new terms and ideas and should all be worked. More general problems appear at the ends of the chapters. The answers to the drill problems are given in the same order as the parts of the problem.] I D1.1. Given points M(-1, 2, 1), N(3, -3, 0), and P(-2, -3, -4), find: (a) RMN; (b) RMN + RMP; (c) |гм; (d) amp; (e) | 2rp - 3rNl. Ans. 4ax-5ay - az; 3ax - 10ay - 6az; 2.45; -0.14ax -0.7ay -0.7az; 15.56 1.5 THE VECTOR FIELD We have defined a vector field as a vector function of a position vector. In general, the magnitude and direction of the function will change as we move throughout the region, and the value of the vector function must be determined using the coordinate values of the point in question. Because we have considered only the rectangular coordinate system, we expect the vector to be a function of the variables x, y, and z. If we again represent the position vector as r, then a vector field G can be expressed in functional notation as G(r); a scalar field T is written as 7(r). If we inspect the velocity of the water in the ocean in some region near the Thus, B = B. ap y(ax a)x(ay. a) =-y sin - x cos = -p sin² -p cos² = -p B = -pa + zaz = 4.4. = = D1.5. (a) Give the rectangular coordinates of the point C(p -115°, z= 2). (b) Give the cylindrical coordinates of the point D(x -3.1, y = 2.6, z=-3). (c) Specify the distance from C to D. Ans. C(x=-1.860, y = -3.99, z = 2); D(p = 4.05, = 140.0°, z=-3); 8.36 41)) g these results, we have G =r cos e cos (sin cot o a, + cos 0 cot o ao - 8%) = A describes the general curvilinear coordinate system of which the ircular cylindrical, and spherical coordinate systems are special cases. on of this appendix could well be scanned now. ENGINEERING ELECTROMAGNETICS I D1.7. Given the two points, C(-3, 2, 1) and D(r =5,0=20°, 6=-70°), find: (a) the spherical coordinates of C; (b) the rectangular coordinates of D; (c) the distance from C to D. Ans. C(r= 3.74, 0 = 74.5°, = 146.3°); D(x = 0.585, y=-1.607, z = 4.70); 6.29