Generating plane equation from LinearSolve

Question

I will ask a simple question and might have an issue on the site that explains better about it, but not found.

I am formulating a code that defines me an equation that I can generate a plot.

m = {{1, 1, 1}, {1, 2, 3}, {1, 4, 9}};
b = {1, 2, 3};
abc=LinearSolve[m, b]
f=abc[[1]]*x+ abc[[2]]*y+ abc[[3]]*z
sol=Solve[f==0,z]
Plot3D[sol,{x,0,15},{y,0,15}]

Or

Plot3D[z,{x,0,15},{y,0,15}]

I'm realizing that there is a mistake, but I do not know how to get an equation from LinearSolve output.

Young · Accepted Answer · 2016-07-14T23:27:52.057

3

Solve is one of the functions that returns a list of rules and you need to use the /. Replace All command. Read: http://support.wolfram.com/kb/12505

m = {{1, 1, 1}, {1, 2, 3}, {1, 4, 9}};
b = {1, 2, 3};
abc = LinearSolve[m, b]
f = Dot[abc, {x, y, z}]
sol = Solve[f == 0, z]
Plot3D[z /. sol, {x, 0, 15}, {y, 0, 15}]

And as J.M. mentioned f= Dot [abc, {x, y, z}]is the same as f = abc[[1]]*x + abc[[2]]*y + abc[[3]]*z

edited Jul 14 '16 at 23:27

answered Jul 14 '16 at 23:21

Young

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You can use Dot[] to form the equation, of course. – J. M.'s missing motivation Jul 14 '16 at 23:24
Really! Sometimes the answer is so easy that does pass shame. – LCarvalho Jul 14 '16 at 23:27
@LeandroMacieldeCarvalho No worries. Glad to help. – Young Jul 14 '16 at 23:32
I would get another plane forming an angle of 50 ° with this plane and had the point {1, 1, 1} and the point {1, 2, 3} in common – LCarvalho Jul 14 '16 at 23:46
I do not have a diagram. I imagined getting through a rotation matrix – LCarvalho Jul 15 '16 at 00:02
https://en.m.wikipedia.org/wiki/Rotation_matrix – LCarvalho Jul 15 '16 at 00:19
https://reference.wolfram.com/language/ref/RotationMatrix.html – LCarvalho Jul 15 '16 at 00:25
@Leandro, you know RotationMatrix[] is built-in, no? Do you know how to work with the Hessian form of a plane? – J. M.'s missing motivation Jul 15 '16 at 00:25
I know, but I can not use it to get the equation of another plan that I want to get – LCarvalho Jul 15 '16 at 00:28
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http://mathematica.stackexchange.com/questions/1457/how-do-you-draw-the-plane-on-which-two-vectors-lie – Young Jul 15 '16 at 00:30
I do not know this Hessian form. – LCarvalho Jul 15 '16 at 00:31
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"I do not know" - it was a hint for you to search the terms in a fabulous search engine, @Leandro. – J. M.'s missing motivation Jul 15 '16 at 00:43
I am Brazilian and sometimes I do not understand what you are writing – LCarvalho Jul 15 '16 at 00:48
http://mathworld.wolfram.com/HessianNormalForm.html – LCarvalho Jul 15 '16 at 00:52
@J.M. I think now I understand what you mean – LCarvalho Jul 15 '16 at 00:55
@Young The link you left helped me a lot – LCarvalho Jul 15 '16 at 01:14
To skip Solve[] altogether: sol = Expand[-Most[abc].{x, y}/Last[abc]]. – J. M.'s missing motivation Jul 17 '16 at 13:27

Generating plane equation from LinearSolve

1 Answers1