Re: easy plane normal vector question

*To*: mathgroup at smc.vnet.net*Subject*: [mg89722] Re: easy plane normal vector question*From*: will parr <willpowers69 at hotmail.com>*Date*: Thu, 19 Jun 2008 05:41:33 -0400 (EDT)

thanks for your response, I found it very helpful. I am still struggling with the problem, although now I am having trouble with displaying the vector. So, I have got this far: plane = 4.07919+ 0.0764884 x - 0.0632675 y Following your advice: vector = Flatten[{Coefficient[#, {x, y}] & /@ {plane}, -1}]; normaliseVec[v_] := v/Sqrt[v.v]; normVector = normaliseVec[vector] {0.0761143, -0.0629581, -0.995109} then to display the vector and the plane, using some 3D arrow code: Between[a_, b_, x_] := b - (b - a)/Norm[b - a]*x; Cone3D[s_, e_, w_] := Module[{v, b, b1, b2, A, r}, v = e - s; A = RotationMatrix[\[Pi]/10, v]; b = {v[[2]], -v[[1]], 0}; b = b/Norm[b]*w; r = {}; For[i = 0, i < 20, i++, b1 = RotationMatrix[i*\[Pi]/10, v].b; b2 = RotationMatrix[(i + 1)*\[Pi]/10, v].b; AppendTo[r, Polygon[{e, s + b1, s + b2}]]; AppendTo[r, Polygon[{s, s + b1, s + b2}]];]; r]; Arrow3D[s_, e_, cw_, aw_, al_] := Module[{m}, m = Between[s, e, al]; {Cylinder[{s, m}, cw], Cone3D[m, e, aw]}]; centroid ={-5.43852, 2.62127, 3.49737} (*I think this might be where i went wrong*) arrowEnd = centroid + normVector now to display: Show[Graphics3D[{EdgeForm[], Red, Arrow3D[centroid, arrowEnd, 0.09, 0.3, 0.5], AspectRatio -> Automatic}, Boxed -> False], Plot3D[plane, {x, -11.1, -0.71}, {y, -1.86, 7.83}, PlotStyle -> Directive[Red, Opacity[.5]], Mesh -> None], Boxed -> False, Axes -> True, AxesLabel -> {"x", "y", "z"}, AxesEdge -> {{-1, -1}, {-1, -1}, {-1, -1}}, PlotRange -> All, ImageSize -> 300, BoxRatios -> 1, AspectRatio -> 1, ViewPoint -> {0, Infinity, 0}] if you then manipulate the image, you can see that the arrow does not appear to be perpendicular to the plane... any suggestions would be very welcome, thank you again, Will