1. Consider the R² - R function f(x,y) = x² + y² +1. (a) Find the Cartesian equation for the plane tangent to the graph of f, at the point where f(x, y) = (1 , 1). (5 marks)

2. Consider the following three points in R³: a(1, 3 , 1) , b (2,0,2), c (3,2,1) (a) Determine whether the three points are collinear, i.e. whether all three lie on the same line. (4 marks) (b) Find an equation for the line L through the point a that is perpendicular to the plane that contains the three points a , b and c . (6 marks)