4. Points P(1, 2, 0), Q(2, 3, -1) and R(-1, 1, 5) lie on a plane. Find the Cartesian equation of the plane. Hence, determine the angle between the straight line=¹=1 y+4 = x-1 2 Z-2 2² and the plane.

Find a general equation of the plane through the point (2, 9, 6) and parallel to the plane x + 5y + 3z+ 4 = 0. Equation:

5. (a) (i) Find the equation of the plane II through the points (1, 1, 1), (1,3,2), and (2,2,0). (ii) Find the equation of the line I through the points (3, 3, −3) and (2, 4, −2). (iii) Find the point where I and II intersect. (iv) Find the angle between II and I (in radians to 1 decimal place). (b) Sketch the curve with polar equation r = sin(30), 0 ≤ 0 < 2π, plotting all the points with r both positive and negative and including explanations for your answer. Do we get any extra points if we allow negative r?

Please don't provide handwritten solution.