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

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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