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3 Equations - 3 Variables

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3 Equations - 3 Variables

Hello guys,

   I'm doing a geometrical calculation program in excel, and for that, I'm using Mathcad to define the formulas.

   For the last one, I have 3 known distances in R3, and 3 coordinates, and I want to find the last one.

   So , the formulas are:

    All the variables are input given, but (a, b, d), which are the last point coordinates (x,y,z).

    I need to get the formulas, a, b, d only in function of the given variables.  So a symbolic solution someway like that:

    a = t+ w-j +2 o.....

    b = o+ n-j +2 w.....

    c = w+ t-j +2 j.....

   I'm very unexperient with Mathcad, so I don't know any function that could do this automaticly for me.  

1 ACCEPTED SOLUTION

Accepted Solutions
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Re: 3 Equations - 3 Variables

By predefining some constants you can get a symbolic representation of the solutions for a, b and d.  See how these are developed in the attached.

Alan

View solution in original post

16 REPLIES 16
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Re: 3 Equations - 3 Variables

Seems like a simple question. The answer is not easy. My computer is crunching at the moment.

I suspect that IF it gives an answer, you will not like to implement it in excell, as it's going to be big formulae.

Anyway. I suspect that you are looking for fully real answers ( all imaginary parts equal to zero ), am I right?

Luc

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Re: 3 Equations - 3 Variables

Here you go:

Now we need to get the three (?) components.

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Re: 3 Equations - 3 Variables

Hey Luc, thank you.

If the formula is huge, I can split it in various short parts to write in excel. This will be no problem.

I'm getting the same error! I really don't matter if it's 1 meter lenght, but I need the formulas.

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Re: 3 Equations - 3 Variables

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Re: 3 Equations - 3 Variables

You are right. As it's a geometrical problem, I'm not looking for imaginary numbers.

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Re: 3 Equations - 3 Variables

Valery, can you please send me your file?

There are somethings that I'm not understanding.

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Re: 3 Equations - 3 Variables

I'm afraid it's not symbolically solvable. Here you have part of an anaylsis:

And it goes on like:

The expression above is about 7 pages wide. Then to calculate d gives an expression that is too big to copy into this field, I cannot even find a way to count the pages, but I'm guessing it's over 50 pages wide....for two possible values of d (due to the squares)... and they aren't explicit... d still depends on b and a....

For symbolics I think you're out of luck here.

But once you fill in numbers, there's little trouble to get answers. Here's an example:

Note that there are 2 solutions each for a, b and d. The top row holds one set of them, the bottom row holds the other set.

Considering you know the numbers, I'd suggest you do the calculation in Mathcad.

Success!

Luc

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Re: 3 Equations - 3 Variables

By predefining some constants you can get a symbolic representation of the solutions for a, b and d.  See how these are developed in the attached.

Alan

View solution in original post

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