S: 91 +9-4= = 36 dy: d: da: x = -21, y = 2. = -3t P = (0,2/2.3) droite passant pas les points P et Q x=1-31, y = 3+1, 2= -3t Q=(22,0,-3) Consider the surface S, the points P, Q and R as well as the lines d1, d2 and d3 whose equations have been distributed to you. (a). Using software like Nspire, draw the surface S with a high transparency index. Also draw at least 3 of its traces (these curves are also called cross sections) specifying for each one whether it is a circle, an ellipse, a straight line or a hyperbola: x = C1, y = C2, z = c3 (where the c; are nonzero constants of your choice). Give the name of the surface s, by consulting the table of quadrics on page 679 of the textbook. Provide a parametrization of each curve. The ExampleTraces tos file could help you! We can make do with an "imperfect" graph. For example, if you use function mode, the surface may appear to be in two pieces when it is not... R=(2.-3.4) (b) On the same graph, draw the points (small spheres) P. Q and R to see if they seem to belong to the surface S or not. (Use the parametrization of the sphere presented in class at period Pl, or that of page 729 by replacing op by u, 8 by t, a by the value of the small radius chosen, and moving the center to the desired point.) For each points P. Q and R, verify by a calculation whether or not the point is on the surface. (c) Give the parametric equations of the line d1. (d) On the same graph, draw the lines d1 to d3. These lines seem to lie entirely on the surface S. In other words, these lines seem to correspond to beams that could be used to build the surface S. Check, with the help of calculations made by hand, if the line d3 is entirely on the surface S. (e) Do lines d1 and d2 have a point in common? If yes, give their point of intersection and calculate the angle formed by the lines. Otherwise, determine if the lines are distinct parallels or if they are left. (f) Do lines d2 and d3 have a point in common? If yes, give their point of intersection and calculate. the angle formed by the lines. Otherwise, determine if the lines are distinct parallels or if they are left. (g) Calculate the distance between the lines d1 and d3, as well as between the lines d2 and d3. (h) Print your graph and add labels by hand to identify the objects.