10 Given are: Points M = (-8,7,-1), Q = (16,33,15), R = (-14,-17,5), Planes E: -x - 2y + z = -7 and F: 2x + y + 4z = 5.

The line h contains the points Q and R. The line intersects the plane F at a point S.

i) Find the coordinates of S.

ii) Circle k is centered around M, and is positioned such that it just touches the line g. The radius of this circle is the shortest distance from M to g. Point S is the tip of an oblique cone with the circle k as the base. Determine the angle of the connection SM to the plane E

iii) Determine the height and volume of the cone

iv) The point S is projected onto the E plane. Is the projected point S' inside or outside the circle k? Justify your answer