a) You are given the vector v=(1,1). Using a matrix that translates by 2 units in both the x and y directions, demonstrate that homogeneous coordinates prevent an illegal transformation for vectors. ( 6 marks) In a 3D animation, a ball with initial position P=(6,3,2) and velocity v=(2,1,2) is moving towards a mesh that is centred at (0,0,0). The ball will hit a face of the mesh defined by the three points {(0,4,0),(4,0,4),(4,0,4)}. b) Calculate the outward normal to the face (outward relative to the mesh center). Show your working. c) How many frames does it take to hit the face? Show your working. (8 marks) (8 marks) d) Calculate the reflected velocity after impact. Show your working. (4 marks)