Q1. A diet is to contain atleast 10 units of vitamin A, 12 units of vitamin B and 8 units of calcium. Two foods f 1 and f 2 are available. A unit of food f 1 contains 1 unit of vitamin A, 2 units of vitamin B and 3 units of calcium and a unit of food f 2 contains 2 units of vitamin A, 2 units of vitamin B and 1 unit of calcium. If one unit of food f 1 costs Rs 16 and one unit of food f 2 costs Rs 20, find the least cost of the mixture which will produce the desired diet. Solution Problem can be represented as Minimise z = 16x + 20y st x + 2y 10 2x + 2y 12 or x + y 16 3x + y 8 x 0, y 0 Corner Poi...
Q1. Find the angle between any two diagonals of a cube. Solution Let O, one vertex of a cube, be the origin and three edges through O be the Co-ordinate axes. The four diagonals are OP, AA', BB' and CC'. Let 'a' be the length of each edge. Then the co-ordinates of P, A, A' are (a, a, a), (a, 0, 0), (0, a, a). The direction ratios of OP are a, a, a. The direction cosines of OP are . Similarly, direction cosines of AA' are . Let be the angle between the diagonals OP and AA'. Then ...