6 m 5m B 4 m F = 400 N C 6. (i) Find the equation of the plane which passes through the three points in the figure. Express the equation

in both vector and Cartesian form. [5 marks] (ii) Determine the equation of the line passing through Calong the direction of the force, which is perpendicular to the plane formed by points A, B & C. [2 marks] (iii) Two long straight pipes are specified using Cartesian co-ordinates as follows: Pipe A: diameter 0.8; axis through points (2, 5, 3) and (7, 10, 8). Pipe B: diameter 1.0; axis through points (0, 6, 3) and (-12, 0, 9). Do the pipes need re-aligning to avoid intersection? [5 Marks]