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I'm trying to plot a normal vector to a plane. I know I'm doing something I should know better, but can't seem to find. Vectors {0, 1, 2}, {1, 1, 3} obviously determine a plane. Their Cross Product is {1, 2, -1}, which is normal. Unfortunately this code (all from the origin):

Graphics3D[{{Blue, Arrow[{{0, 0, 0}, {0, 1, 2}}]}, {Red, Arrow[{{0, 0, 0}, {-1, -2, 1}}]}, 
{Blue, Arrow[{{0, 0, 0}, {1, 1, 3}}]}}]

Yields,

enter image description here

Which doesn't look quite right. Just don't trust pictures? Any thoughts appreciated. Trying a different way I found some Mathematica code from a multivariable course for normals to a plane... and I got the same thing...

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  • $\begingroup$ Check BoxRatios. $\endgroup$
    – David G. Stork
    Commented May 3, 2021 at 18:11
  • $\begingroup$ This is great, thank you! $\endgroup$
    – Gerald Bilodeau
    Commented May 3, 2021 at 20:13

2 Answers 2

Reset to default
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v1 = {0, 1, 2};
v2 = {-1, -2, 1};
v3 = Cross[v1, v2];
origin = {0, 0, 0};

Graphics3D[
 {Opacity[0.5], InfinitePlane[origin, {v1, v2}], Opacity[1],
  Blue, Arrow[{origin, v1}], Arrow[{origin, v2}],
  Red, Arrow[{origin, v3}]},
 PlotRange -> {{-5, 5}, {-5, 5}, {-5, 5}}, ViewPoint -> {1, -3, 1}]

enter image description here

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Using option AspectRatio we can adjust the picture

Graphics3D[{{Blue, Arrow[{{0, 0, 0}, {0, 1, 2}}]}, {Red, 
    Arrow[{{0, 0, 0}, {-1, -2, 1}}]}, {Blue, 
    Arrow[{{0, 0, 0}, {1, 1, 3}}]}}, AspectRatio -> 1, Axes -> True, 
  AxesLabel -> {"x", "y", "z"}, AxesStyle -> RGBColor[0, 0, 0], 
  BaseStyle -> 12]

enter image description here

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