A cone being intercepted by a slanted plane

I have the 3d cone:

Plot3D[-Sqrt[x^2 + y^2], {x, -20, 20}, {y, -20, 20}, Mesh -> None,
BoxRatios -> {1, 1, 1}]

I need a slanted plane intersecting it. Can somebody help me?

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2

 

Add a plane to your plot? e.g. Plot3D[{-Sqrt[x^2 + y^2], -1 – x – y}, {x, -1, 1}, {y, -1, 1}]
– 2012rcampion
Feb 26 ’15 at 0:10

1

 

I don’t quite get what you’re after. You know the equation of a cone but not of a plane? Any linear function of x and y yields a plane.
– Michael E2
Feb 26 ’15 at 0:19

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2 Answers
2

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Graphics3D[
{
{Opacity[0.5], Cone[{{0,0,0}, {0,0,3}}, 1]},
{Yellow, Opacity[0.5], Polygon[{{-1,-1,1}, {-1,1,1}, {1,1,2}, {1,-1,2}, {-1,-1,1}}]}
}
]

Or play around with this:

Manipulate[
Graphics3D[
{
{LightBlue, Opacity[0.5], Cone[{{0, 0, 0}, {0, 0, 3}}, rcone]},
{Yellow, Opacity[0.5],
Polygon[{{-1,-1,1}, {-1,1,1}, {1,1,m}, {1,-1,m}, {-1,-1,1}}]}
}
],
{rcone, .5, 2}, {m, 1, 3}
]

let’s say you have a plane:

myPlane=-8-x-2y

you can use Plot3D like so;

Plot3D[{-Sqrt[x^2 + y^2], myPlane}, {x, -15, 15}, {y, -15, 15},
Mesh -> None, BoxRatios -> {1, 1, 1}, PlotLegends -> “Expressions”]

you can pimp your plot with RegionFunction:

Plot3D[{-Sqrt[x^2 + y^2], myPlane}, {x, -15, 15}, {y, -15, 15},
RegionFunction -> Function[{x, y, z}, -10 < z < 10], BoxRatios -> 1,
PlotLegends -> “Expressions”]

and or and specify ViewPoint for visualization: