1. Consider the conic C with equation: 2+2√3ry-y=2. Find the discriminant of C and hence state what kind of conic it is. 2. The plane II contains the points (1,2,3), (0,1,2) and (2,3,0). The line L passes through the points (2,0,0) and (5, 2,0). (a) Find an equation of II, and, as a check, verify that the three points (1,2,3), (0, 1, 2) and (2,3, 0) all satisfy the equation you give. (b) Find a parametric equation of L. (c) Find the point X where II and L meet. (d) Find the angle between II and L in radians, correct to 2 decimal places. 3. Suppose that a plane has equation 2x+3y+4z = 9. (a) Find two points on the plane with integer coordinates. (b) Find the parametric form of the line between the two points you gave in (a). (c) Show that the line you gave in (b) is orthogonal to the vector (2,3,4). 4. A regular tetrahedron has vertices at the points A = (1, 1, 1), B = (1,-1,-1), C=(-1,1,-1) and D = (-1, -1, 1). (a) Show that the line through OA is orthogonal to the plane containing the face BCD. Deduce that the line containing the origin and any vertex is orthogonal to the plane containing the other three vertices (without checking this case-by-case). (b) Show that the angle between the planes containing the faces ABC and BCD is cos(). Explain why it follows that the angle between the planes containing any two faces is cos (4) (c) Find the angle between the line through the edge AB and the plane containing the face BCD, correct to 2 decimal places. 5. A truncated octahedron is a polyhedron with 14 faces, of which 6 are squares and 8 hexagons. How many edges does a truncated octahedron have? How many vertices?