Question 1 (32 marks) a. For the points P(1,{},1), Q(2,-1,2), and R(1,2,[}): i. Find the parametric equation for the line passing through P and R. (2 marks) Find the normal equation of the plane through P, Q and R. (3 marks) b. Let f(x_.y)=ln(4x2y2). i. iii. State the domain of f(x, 3;) and sketch it neatly in the xy-plane. The domain must be expressed in set notation eg. domf : {(x,y) E R2 : _ _ _}. (2 marks) State the range of f and indicate it on a neat sketch of the real line. The range must be expressed in set notation eg. R(f) = {x E R : __ _} or RU") 2 some interval or union of intervals. (2 marks) Tip: Examples of nding and sketching the domain and range of a function of two variables can be found in the lecture notes and Chapter 14 of the textbook. On the same xy axes, make a neat hand-drawn sketch of the level curves of the function for : : 1, 0 and 1. You must show all working used to determine the shape of the curves, and label all important features such as the axes, intercepts and the associated : value. Note: this must be a new set of axes, do not reuse the axes 'om (i)