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) [5T]

1: + 4 + 3 5 = 0

2: + 3 + 2 4 = 0

3: + + 1 = 0

7. Lucas does not like Dustin weapon and decides to design his own. His model has a plane that contains the point (5,2, 4) and two direction vectors, = (4,8,1)and = (3, 2,0). Which of the following statement(s) about this plane is/are true? Justify your answer. [4T,1C]

i. The plane has a parametric equation that can be defined as follows: { = 5 + 4 3 = 2 + 8 2 = 4 + +

ii. The plane has a vector equation that can be defined as (, , ) = (5,2, 4) + (3,2,0) + (4,8,1)

iii. The point (31,6,0) lies on the plane iv. The -intercept of the plane is 0,0, 5)