MAS130: Calculus & Matrix Algebra OUA Study Period 3, 2018 ASSIGNMENT 4 Due by 4 pm (AWST), Wednesday, November 7 Total Marks: 50 Show all working and give answers exactly where possible. 1. [12 marks] If a = (3, 1, 3) and b = (4, -1, 8), find |a|, |b|, 3a – b, a · b, a × b and b × a. What is the angle between a and b? 2. [11 marks] For the triangle ABC, with vertices A = (2, -2, 3), B = (5, 1, 6) and C = (8, v, 3), find (a) the length of side AB, (b) the equation of the line that passes through A and B, (c) the value of v so that the angle at point B is p/3. 3. [7 marks] Solve the following system of equations using row reductions (Show all working). 2x + 4y + z = 29, x + y + 2z = 7, x + y + 3z = 6. 4. [10 marks] Use row operations (show all working) to compute the inverse of the matrix A. Show that it is correct (to get full marks you must do this). A = ? ?? 2 4 5 4 4 6 2 2 1 ? ?? 5. [5 marks] Find the equation of the plane containing the vectors a = (1, 2, 4) and b = (6, -1, 4) and the point A(6, 7, -3). 6. [2 marks] Find the equation of the line from A(1, 7, -6) to B(-1, -2, -1) in parametric form. 7. [3 marks] Suppose a jump-jet takes off perpendicular to the deck of an air-craft carrier whose surface is described by 2x-5y + 6z = 14. In what direction will it launch? If it takes off vertically (in the direction of k), what is the angle between this direction and the normal to the deck? Document Preview:

MAS130: Calculus & Matrix AlgebraOUA Study Period 3, 2018ASSIGNMENT 4Due by 4 pm (AWST), Wednesday, November 7 Total Marks: 50Show all working and give answers exactly where possible.1. [12 marks] If a = (3; 1; 3) and b = (4;