I need solve this assignment

Question 1 (20 points) (a) (10 points) Find an equation of the sphere that passes through the point (3, 3, 2) and centered at the point (2, -2, ~3). (b) (10 points) Show that the following equation represents a sphere, and nd its center and radius, m2+y2+z26x+4y4z+1320. Question 2 (20 points) Consider two points in the 3-dirnentional space, A(1,1,1), B(3,2,2). (a) (15 points) Find the vector equation and parametric equation of the line that passes through the points A and B. (b) (5 points) At what point does the line found in (a) intersect the any-plane? Question 3 (20 points) Consider a plane 23: + 3y Bz = 5 andaline 3323275, y=4t3, z=2t5. (a) (10 points) Find the angle between the normal vector of the plane and the direction vector of the line. (b) (10 points) Find the point at which the line intersects the plane