# Applications of vectors and trigonometry to 3d cubes help??

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• Aug 23rd 2013, 08:14 PM
cchloe93
Applications of vectors and trigonometry to 3d cubes help??
Hi. So I need help with some math questions. I've asked my friends but they're kind of stuck too.

1.http://s1295.photobucket.com/user/chloe ... 5.png.html
It is supposed to be a cube that is sticking out of the ground. We were given:
The ground coincides with the x,y-plane and that the y-axis is supposed to point West and the x-axis North
A = (12.9258, 31.0732, 8.8878) and C = (2.1003, 4.5653, 17.4866)
B and D are at equal height above the ground
And all these numbers are measurements in meters

So I've managed to find the other points:
A=(12.9258,31.0732,8.8878)
B=(-6.9962,21.4153,13.1872)
C=(2.1003,4.5653,17.4866)
D=(22.3976,19.1976,13.1872)

A'=(12.6675,27.6495,0)
B'=(-7.3795,16.3354,0)
C'=(1.5921,-2.1709,0)
D'=(22.0143,14.1177,0)

|AA'|=9.5279m
|BB'|=14.1370m
|CC'|=18.7461m
|DD'|=14.1370m
|AB|=22.5532m

〖Area〗_A'B'C'D'=378.5771m^2

But I still cannot figure out how to determine the volume of the cube above and below the ground. At first i thought the volume of cube above was split into two parts, a rectangle and a triangle, but then I thought it could be a trapezoid? I've tried using both formulas, but I still cant seem to wrap my head around it. I've found the volume of the total cube to be 11471.54017m^3. Using the formula for the volume of a trapezoid i ended up with a value much larger than the volume i got for the cube itself!

2.http://s1295.photobucket.com/user/chloe ... 9.png.html

This is another cube (Cube2) that has the same dimensions as the one above. It will be sunk into the ground such that the center of the cube is at ground level and such that one of the four diagonals of Cube2 is at right angles to the ground.

If the sun is right above, what shape is the shadow that Cube2 casts? Sketch this shadow.

So I found out that where the water intersects it creates a hexogonal shape, and my friends say its supposed to be a nonagonal shape shadow but I don't see it.

Thanks you so much for helping!