3. A point P(3,0,5) lies on a plane that can be defined by the scalar equation Ax + By + Cz + D = 0. A normal vector, n, to this plane is (2, -3,1). Find the scalar equation. 4. How many solutions are there between the plane P1: (x, y, z) = (4, -3, -1) + s(1, -3,1) + t(2,4, -3) and the line L1: (x, y, z, ) = (3,1 - 2) + k(-1, -1,1)? If there is/are solutions, find the value of the solution(s). 5. How many solutions are there between planes P1: 2x - y + 2z = 2 and P2 : - x + 2y + z = 1? If there is/are solutions, find the value of the solution(s). 6. Dustin is trying to design a weapon to fight the Demogorgon. His model has three planes, and he needs to figure out their configuration. He thinks they intersect in a line or at a point. Is he correct? Justify your answer. If there is/are solutions, find the value of the solution(s) P1:x+ 4y + 3z - 5 =0 P2: x+ 3y+ 2z - 4 = 0 P3:xty- z+1=0