Solve the following:
Q: You are given the vectors
X = (1,1,1), y = (2,1,1) and z = (6,2,2).
(i) Find the Cartesian equation of the plane Π normal to the vector x containing the point (2,1,1).
(ii) Find the parametric equation of the line l through the points (2,1,1) and (6,2,2).
(iii) If l' is given parametrically by l' = x + ty (with x and y defined above), find the point of intersection of l' with the plane Π.
(iv) Find x x y, y x z and [x, y, z].
Give an explanation in geometric terms of what you have found.