The plane π has vector equation r=(-2i+3j-2k)+λ(2i+3j+2k)+μ(6i-3j+2k).
i) Illustrate that Cartesian equation of plane π is 3x+2y-6z=12.
ii) Plane π meets x,y and z axes at A, B and C respectively. Determine coordinates of A, B and C.
iii) Determine the Volume of pyramid OABC.
iv) Determine angle between plane π and x-axis.
v) Therefore, or otherwise, compute distance from origin to plane π.
vi) Using the answers from (c) and (e), determine area of triangle ABC.