Calculating G's Distance from BH on an ABCD.EFGH Cube

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In summary, the distance between the point G and the line BH in an ABCD.EFGH cube with side length 8 is $\frac{8}{3}\sqrt6 cm$. The options provided do not include this answer.
  • #1
Monoxdifly
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In an ABCD.EFGH cube whose side length is 8, the distance between the point G and the line BH is ...
A. 4 cm
B. \(\displaystyle 4\sqrt2\) cm
C. \(\displaystyle 4\sqrt3\) cm
D. \(\displaystyle 8\sqrt2\) cm
E. \(\displaystyle 8\sqrt3\) cm

I got \(\displaystyle \frac{8}{3}\sqrt6\) cm. Do you guys get the same answer?
 
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  • #2
Monoxdifly said:
In an ABCD.EFGH cube whose side length is 8, the distance between the point G and the line BH is ...
A. 4 cm
B. \(\displaystyle 4\sqrt2\) cm
C. \(\displaystyle 4\sqrt3\) cm
D. \(\displaystyle 8\sqrt2\) cm
E. \(\displaystyle 8\sqrt3\) cm

I got \(\displaystyle \frac{8}{3}\sqrt6\) cm. Do you guys get the same answer?
I agree with you: $\frac83\sqrt6$. It's odd that in two separate problems the answer does not appear in the list of choices.

I am getting these answers on the assumption that "an ABCD.EFGH cube" means a cube where the base is ABCD, and the upper vertices are above the corresponding lower ones, so that EA, FB, GC and HD are the vertical sides. Presumably that is what is intended?
 
  • #3
Opalg said:
I am getting these answers on the assumption that "an ABCD.EFGH cube" means a cube where the base is ABCD, and the upper vertices are above the corresponding lower ones, so that EA, FB, GC and HD are the vertical sides. Presumably that is what is intended?

Yes, that is what's intended.
 

Related to Calculating G's Distance from BH on an ABCD.EFGH Cube

1. How do you calculate the distance from a black hole to a point on an ABCD.EFGH cube?

To calculate the distance from a black hole to a point on an ABCD.EFGH cube, you can use the formula: D = √(x2 - x1)2 + (y2 - y1)2 + (z2 - z1)2, where D is the distance, x1, y1, and z1 are the coordinates of the black hole, and x2, y2, and z2 are the coordinates of the point on the cube.

2. Can you calculate the distance from a black hole to multiple points on an ABCD.EFGH cube?

Yes, you can calculate the distance from a black hole to multiple points on an ABCD.EFGH cube by using the same formula mentioned in the previous question. Simply plug in the coordinates of each point on the cube and the coordinates of the black hole to find the distance for each point.

3. How does the distance from a black hole to a point on an ABCD.EFGH cube affect the gravitational force?

The gravitational force between a black hole and a point on an ABCD.EFGH cube is inversely proportional to the square of the distance between them. This means that as the distance increases, the gravitational force decreases.

4. Is the distance from a black hole to a point on an ABCD.EFGH cube the only factor that affects the gravitational force?

No, the distance is not the only factor that affects the gravitational force. The mass of the black hole and the mass of the point on the cube also play a role in determining the strength of the gravitational force between them.

5. How can the distance from a black hole to a point on an ABCD.EFGH cube be used in scientific research?

The distance from a black hole to a point on an ABCD.EFGH cube can be used in various scientific research studies, such as studying the effects of black holes on nearby objects, understanding the structure and behavior of black holes, and testing the principles of general relativity. It can also be used in space exploration to determine safe distances from black holes for spacecrafts.

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