Consider a rectangular coordinate system with its origin at the center of the earth, z-axis through the North Pole, and x-axis through the prime meridian. Find the rectangular coordinates of Sydney, Australia (34° S, 151° E), and Bogot´a, Colombia (4°32 N, 74° 15 W). A minute is 1/60°. Assume that the earth is a sphere of radius R = 6370 km.