i need help with maths.
involves a sunken cube, example of a sunken cube is the one at the melbourne museum; http://maps.google.com.au/maps?hl=en...0109985&li=lmd
and zoom to check it out.
now what my math project asks:
Imagine that you are the person in charge of creating a 3d image of the Cube for Google Earth. For this you need to find 3d coordinates of the corners of the top square A,B,C,D, as well as the coordinates of the points A',B',C',D' at which four edges of the Cube intersect the ground. Here A is supposed to be connected to A' by such an edge (see the left photo) and similarly for B and B', C and C', and D and D'.
You are not the first person to attempt finding these coordinates. In fact, the last person who tried just got fired yesterday because he was not able to do the job. You’ve just taken over and you are supposed to base your work on your predecessors notes.
His notes are a mess, but it is clear that he started by letting the ground coincide with the x, y-plane and that the y-axis is supposed to point West and the x-axis North. It is not clear where exactly the origin of his coordinate system is, but wherever it is, in this coordinate system B = (3.1319, 22.5477, 12.1303), D = (30.2051, 13.9229, 12.1303) and B' = (2.3308, 20.0329, 0.0). Finally, it is also clear that all these numbers are measurements in meters. Off you go!
Wait, apart from finding those eight coordinates I would also like you to figure out how long one of the sides of the Cube is; what the lengths of the segments AA',BB',CC',DD' are; what the area of the quadrilateral A',B',C',D' is; and what the volumes of the parts of the Cube above and below the ground are.
so need to calculate:
A = (?, ?, ?))
B = (3.1319, 22.5477, 12.1303)
C = (?, ?, ?))
D = (30.2051, 13.9229, 12.1303)
A' = (?, ?, ?)
B' = (2.3308, 20.0329, 0.0)
C' = (?, ?, ?)
D' = (?, ?, ?)
|AA'| =?m
|BB'| =?m
|CC'| =?m
|DD'| =?m
sidelength =?m
area(A'B'C'D') =?m^2
volume above =?m^3
volume below =?m^3
Hint: Since we are dealing with a cube that is full of right angles, to quickly check
whether your coordinates for the different points make sense, calculate some the distances
between these points and check that some of the edges defined by them meet at
right angles (using the dot product).