EG 4103 : Maths and Introduction to Fluid Mechanics - Mathematics Assignment

Internal Code: MAS3062

Mathematics Assignment:

Questions: 1) a) if, find the magnitude of , and the unit vector parallel to b) if , find the angle between (part a) above) and to 3 d.p. c) if the points A, B and C (Fig 1.) have coordinates (12,-2,1), (7,6,-2) and (-3,- 6,-1) respectively, find the area of triangle ABC 2) The irregular pentagon, shown in Fig 2 below needs to be rotated through in an anti-clockwise direction about the origin of the system O Using Complex Numbers i) convert each of z1, z2, z3, z4 and z5 into exponential form ii) rotate each point though anti-clockwise iii) convert the results from ii) back into the cartesian form 3) a) Using Cramer’s Rule, or otherwise solve the system of equations for b) By the method of LU decomposition solve the same system of equations