Find Area of Triangle (-1 2 -1 2), (-1 2 -1 1) & (2 -1 2 2)

[kingkong69]

find the area of the triangle with vertices (-1 2 -1 2) (-1 2 -1 1) and (2 -1 2 2)
its 4 d

Im confused
thanks in advance

 

[emailanmol]

OMG! i have never seen something like this before.

Where did you find this question?
You will have to define the 4d space first.

Is the 4th dimension time? Like the Minkowski space.

A google search on area of triangle in 4d yields nothing.

 

[kingkong69]

haha ye I am confused
i was working through maplesoft,
http://img696.imageshack.us/img696/9376/123123123ii.jpg

 

[emailanmol]

Ok i found something.Its not 4d but rather semantics .

http://www.maplesoft.com/support/help/Maple/view.aspx?path=geometry/triangle

 

[kingkong69]

Ok i found something.Its not 4d but rather semantics .

http://www.maplesoft.com/support/help/Maple/view.aspx?path=geometry/triangle

wat semantics?

 

[emailanmol]

Its stated in that webpage.

the fourth co-ordinate is n which signifies the axis.

I cannot elaborate much on how you will attempt the problem as I have no experience regarding maplesoft.

I hope the link helps you with what the four co-ordinates signify

 

[minio]

I would say, that you just need to find length of each side in 4D. From there it is just ordinary triangle.

 

[emailanmol]

I would say, that you just need to find length of each side in 4D. From there it is just ordinary triangle.

How do we find length of each side in 4d?
I think I am learning something new here :-)

 

[minio]

I am definitely no expert so I might be wrong, but I would say that the length would be

\left|AB\right|=\sqrt{(a_{w}-b_{w})^{2}+(a_{x}-b_{x})^{2}+(a_{y}-b_{y})^{2}+(a_{z}-b_{z})^{2}}

 

[emailanmol]

Ok.I think its right by symmetricity.

But my opinion is that its not valid on this question.
Here the 4th coordinate doesn't signify the presence of a 4th dimension. It just represents some co-ordinate axis which the website states.
It is actually stating the coordinates based on some conventions.

 

[dodo]

If you call your three points A=(-1 2 -1 2), B=(-1 2 -1 1) and C=(2 -1 2 2), try to think in terms of the vectors AB and AC (as two of the sides of your triangle). The first thing you may notice is that these two vectors are orthogonal.