19. Let P be the point (4, 1, 2). Find parametric equations for the line through P and parallel to the vector (1, -1, 0). 20. (a) Find parametric equations for the intersection of the planes 2x + y z = 3 and x + 2y + z = 3. (b) Find the acute angle between the two planes. 21. Find an equation of the plane that is parallel to the plane x+5y-z+8=0 and contains the point (1, 1, 4). 22. Find an equation of the plane through the point (4, 3, 0) and parallel to the vectors i + k and 2j - k. 23. What condition must the constants satisfy for the planes a1x+bly + clz=d1 and a2x + b2y + c2z = d2 to be perpendicular? 24. (a) List six common types of quadric surfaces, and describe their traces in planes parallel to the coordinate planes. (b) Give the coordinates of the points that result when the point (x, y, z) is reflected about the plane y = x, the plane y = z, and the plane x = z. (c) Describe the intersection of the surfaces r = 5 and z = 1 in cylindrical coordinates.