Equation of the plane passing through the three points

Question

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How to put terms in lexicographic order?

I write the equation of the plane passing through the three points $A(-1, 5, -2)$, $B(2, 4, -3)$ and $F(4, -8, 6)$, and this is my code

A := {-1, 5, -2};
B := {2, 4, -3};
F := {4, -8, 6};
M := {x, y, z};
u := A - B;
v := A - F;
w := A - M;
n := u\[Cross]v;
Sort[Simplify[w.n] == 0]

I want the equation $ABF$ has the form

$21 x + 29 y + 34 z-56=0$,

but Mathematica out

$0 == -56 + 21 x + 29 y + 34 z$

What must I do? Please help me.

Try PolynomialForm[Simplify[w.n], TraditionalOrder -> True]. — J. M.'s missing motivation, Sep 11 '12 at 10:07

Vitaliy Kaurov · Accepted Answer · 2012-09-11T19:27:45.253

11

It really does not matter how to write these equation - the order does not influence mathematical statement. Your both cases are correct mathematically. Notation/style is a different matter. Use transition to traditional notation:

TraditionalForm[Simplify[w.n] == 0]

enter image description here

To get a better grip on the subject please read Polynomial Orderings.

edited Sep 11 '12 at 19:27

answered Sep 11 '12 at 06:44

Vitaliy Kaurov

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Also, perhaps a warning is in order: tweaking expressions to have Mathematica write them the way you like is many times very difficult. Avoid trying it until you get a good grip. – Dr. belisarius Sep 11 '12 at 07:09
1

@belisarius good point. I add a tutorial link. – Vitaliy Kaurov Sep 11 '12 at 07:15

Equation of the plane passing through the three points

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