1. Given. v = 21 +3j + k and w = 5i +4j -3k, find a vector perpendicular to the plane 2. Let f(o, y) = Arly3 + 3x3y', find: (a) Vf (1, 1) (b) f- (1, 1), where u = j 3. The population density of a circular city of diameter 10 miles varies linearly from 100 people per square mile at the center of the city to 0 people per square mile on the outer boundary. Set up an integral that represents the total population of the city. Evaluate the integral. 4. Make a sketch of the integration region and switch the limits of integration for the following double 1 1 integral. Then evaluate the integral: 5. Evaluate vos +y' dady, where R is the top half of a ring between two circles, one of radius 2 R and the other of radius 3, both centered at the origin. 6. Describe and draw the surface: 0 5 0