Lucas does not like Dustin weapon and decides to design his own. His model has a plane that contains the point A(-5,2, -4) and two direction vectors, AB = (4,8,1)and AC = (-3,-2,0). Which of the following statement(s) about this plane is/are true? Justify your answer. i. The plane has a parametric equation that can be defined as follows: (x = -5+4t - 3s y = 2+8t - 2s (z=-4+t ii. The plane has a vector equation that can be defined as (x, y, z) = (-5,2, -4) + t(3,2,0) + s(4,8,1) iii. The point D (31,6,0) lies on the plane iv. The z-intercept of the plane is 0,0, -5)2. Four students each made a statement about the equation of a line in R2 given in vector form, f" = (3.5) t(2, 3). Which students is/are correct? Justify your answer. i. Eleven: The equation of this line 111 scalar form is 2x + 3y 1: 0 ii. Lucas: A line L, that 15 parallel to the given line 15 as follows: L'{ x = 1 + 2.51: ' y = 8 3.75t iii. Finn: A vector that is perpendicular to the given line is 1-5 = (9, -4-) iv. Dustin: Two points on this line are: (1 ) and (0, 0.5)