Given info: points M = (-8,7,-1), Q = (16,33,15), R = (-14,-17,5) line g: (x,y,z)=(-1,7,6)+t(2,1,4) Plane F: 2x + y + 4z

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Given info: points M = (-8,7,-1), Q = (16,33,15), R =
(-14,-17,5)
line g: (x,y,z)=(-1,7,6)+t(2,1,4)
Plane F: 2x + y + 4z = 5
a) Solve for the equation of a plane E which contains the point
M and line g
b) What is the radius of a circle k which has its midpoint at M,
which just touches the line g?
c) The line h has the points Q and R, and intersects the plane F
at point S. Find the coordinates of point S.
d) The point S is the point of a oblique cone, with the circle k
as its bottom area. Determine the angle between the connection SM
and the plane E (obliqueness of the cone)
e) Find the height h and Volume V of the cone
f) Point S is projected onto plane E. Is the projected point S'
inside or outside the circle k? Justify your answer