I was practicing my tensor analysis and calculated a normal vector to a surface. I wanted to see it looked orthogonal to the surface. It didn't really. So I made a tangent plane to the surface. The normal vector still looks a bit un-orthogonal but it passes all the mathematical tests.

Paraboloid, Normal vector and tangent plane ##\phi_2\left(\vec{x}\right)=\left(x^1\right)^2+\left(x^2\right)^2-x^3=0## |

You can play with this at https://www.math3d.org/ybhLm7KGb and stop it from moving.

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I also used Debut Video Capture to make a .avi from math3d and then cloudconvert.com to make the .gif. It is simpler than ezgif.com.

Other surfaces and vectors:

Plane and normal vectors (not v) Play at https://www.math3d.org/fq5CtGqYa ##\phi_1\left(\vec{x}\right)=x^1+x^2+x^3=5## |

Sine wave with normal vectors Play at https://www.math3d.org/D8xf0gZMT ##\phi_3\left(\vec{x}\right)=x^3+r_0\cos{\left(kx^1\right)}=-4## |

Lots more tools on Physics Forums at