Question 5 (19 Marks) I) Consider the plane in Rs, with scalar equation: 2x + 3y + 4z = 0. a) Show that this plane passes through the origin. b) Write down a normal vector to this plane. Hint: find a vector n such that n. (x - 1) =0. c) Find two other points on the plane, V and W, and their associated vectors v and w, with the property that v and w are not multiples of each other. d) Use v and w to write down the vector equation of the plane. II) Consider the plane in R3, 2x + 3y + 4z = -1. a) Show that this plane does not pass through the origin. b) Find a point P on the plane with associated vector p. c) Write down the equation of the plane in the form n. (x-p=0. d) Write down a normal to this plane. e) What is the geometrical relationship between the two planes in parts I and II of this question. (One sentence answer). f) Find two other points on the plane, V and W, and their associated vectors v and w, with the property that v - p and w - p are not multiples of each other. g) Use v and w to write down the vector equation of the plane. h) Write down a normal to the plane 4x 6y + 172 = 234