Tetrahedron HIJK, H = (4, -1, -3) I = (0, -5, 0) J = (-2, 0, 0), volume 43mm^3; find K

G

Gussy

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Feb 18, 2019
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Hi, I was wondering if there is a formula or some working method where you can determine the vertex of a tetrahedron using its volume? I have scoured the internet to no avail. I will work out the question myself, I'm just needing a headstart.

Question:
For the tetrahedron of HIJK, with a volume of 43mm^3, determine the value of K if:
H = (4, -1, -3)
I = (0, -5, 0)
J = (-2, 0, 0)
K = (?)

Thanks! This is urgent!
 
Last edited:
The fourth vertex could be anywhere on either of two planes parallel to HIJ, at a distance that can be determined by dividing 3 times the volume by the area of triangle HIJ.
 
Hi, do you mind showing this for me? Does it look like 3 * 43mm^3/area ?
 
After doing this I get 7.891 - how do I get it into x, y, z form?
 
As I said, that will be the distance from the plane of the base to the plane in which the other vertex must lie.

How did you calculate the area?

Do you know how to find the equation of the plane containing three points? Do you know how to find the equation of a plane a given distance away from it?

Can you tell us more about your goal (since finding a single point will not be possible)?
 
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