CALCULUSAn economy consists of three sectors: coal, steel, and railroads. To produce one unit of coal requires $\frac{1}{10}$ of a unit of coal, $\frac{1}{10}$ of a unit of steel, and $\frac{1}{10}$ of a unit of railroad services. To produce one unit of steel requires $\frac{1}{3}$ of a unit of coal, $\frac{1}{10}$ of a unit of steel, and $\frac{1}{10}$ of a unit of railroad services. To produce one unit of railroad services requires $\frac{1}{4}$ of a unit of coal, $\frac{1}{3}$ of a unit of steel, and $\frac{1}{10}$ of a unit of railroad services. Determine the production levels needed to satisfy an external demand for 300 units of coal, 200 units of steel, and 500 units of railroad services. LINEAR ALGEBRAFind the norm of v, a unit vector that has the same direction as v, and a unit vector that is oppositely directed to v. (a) v=(3, -5), (b) v=(3, 3, 1). (c) v=(0, 1, -1, 2, 6).