# Tagged Questions

The (3d) tag is for things related to 3-dimensions. For geometry of 3-dimensional solids, please use instead (solid-geometry). For geometry that is not on a plane, but otherwise agnostic of dimensions, perhaps (euclidean-geometry) or (analytic-geometry) should also be considered.

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### Vector equation of line containing point and perpendicular to plane [duplicate]

How would one find the vector equation of the line that contains the point (x0, y0, z0) and is perpendicular to the plane Ax + By + Cz = D?
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### Give a geometric description of the following set of points

Give a geometric description of the following set of points: $x^2 +y^2 + z^2-8x+14y-18z>/= 65$ So I completed the square and got the set to read: $(x-4)^2+(y+7)^2+(z-9)^2>/= 211$ However ...
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### can every object be represented mathematically?

I was just wondering if all 2D/3D objects/images/shapes could be represented by equations. For example, SpongeBob 2D curve and many more. How should I approach, as in, some theories that already exist?...
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### Pizza Delivery along the shortest path

You are the Captain of the USS Gauss and you have been flying in the direction $2 i + j + k$ for quite awhile. You are currently at the point $(6, 3, 3)$. Your helper monkey Mojo just discovered ...
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### rotation to quaternion matrix handeness

I've understand that quaternions do not have handness but rotation matricies derived from unit quaternions does. The following formula is given by wikipedia for quaternion to rotation matrix ...
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### For the points A,B,C,D is given that C belongs to AB, M belongs to AD and D doesn't belong to AB, prove that the plane (ABD) is the same as (CDM)

For the points $A,B,C,D$ is given that $C$ belongs to $AB$, $M$ belongs to $AD$ and $D$ doesn't belong to $AB$, prove that the plane $(ABD)$ is the same as $(CDM)$. Here is drawing: I tried to prove ...
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### Coordinates of circumcentre of an isosceles triangle in 3D

I have an isosceles triangle in 3D and I need to find the coordinates of the circumcentre of this triangle. I know the coordinates of the three vertices. One method I thought of is to solve equation ...
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### How to extract an equation from transformation matrix multiplication?

I am trying to rotate a point in a 3D space in the 3 axis together around a specific origin point. Unfortunately I can't use matrices in my application,All I can do is just the basic math operations (...
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### Prove that if through three given points two planes can be drawn, then infinitely many planes throught these points can be drawn.

Prove that if through three given points two planes can be drawn, then infinitely many planes through these points can be drawn. I don't get how this is possible, since there is unique plane passing ...
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### Text book on solid geometry/stereometry, without involving analytic geometry

As the title says I'm searching for a textbook, about solid geometry, without involving analytic geometry. The material which the book should cover is the stereometry learned in the eastern bloc. An ...
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### Obtain plane equation from the rotating angles that generated it

Consider an $(x, y, z)$ system where positive $x$ points to the right, positive $y$ points upwards, and positive $z$ points outside of the screen. I create a new system $(x', y', z')$ by applying two ...
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### Check Vector3 points on one line using a Matrix

I know that for 3 Vector2 points (say points a, b, c) the determinant of the following ...
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### How to visualize a 3D region plot of an inequality easily?

I can't find the right way to think about the region plot of an inequality. Considering $A=\big\{ (x,y) \in \mathbb{R^2} \mid y<x+1 \big \}$, almost automatically I say: the points "under" the ...
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### Prove that through every point in space, not lying on a given line, there exists a unique line parallel to the given one

Prove that through every point in space, not lying on a given line, there exists a unique line parallel to the given one. let's name the point $A$, the given line $a$, and the searched line $b$. I ...
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### Creating 3D program, view becomes warped if turned

I'm creating a 3D program from scratch in Java, but have become stuck and need help with the math. The way the program works is essentially, there are a 'view from' and a 'view to' point. I use these ...
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### How to proof that two lines in cube are perpendicular, without use of vectors

Given: Cube $ABCDA_1B_1C_1D_1$ Prove that $BD$ is perpendicular to $AC_1$ I don't have any idea how to proof this. Also I can't use vectors(we didn't study them in school). I can use all theorems ...
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### Finding points along a catenary curve

As I am no mathematician, I have been struggling to find an equation to accurately predict points spaced along a curve separated by distance d. Given two points in 3 dimensional space, assume a string ...
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### Center of Arc with Two Points, Radius, and Normal in 3D

I'm struggling to get the math to work out on this. I need to derive an alorithm for a program where I'm representing geometric entities. In this case, it's an arc. I would like to create the arc ...
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### The arctangent is a strange floating point number

I have 2 players in a game (Cod 4). I read X, Y, Z and store them in: ...
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### How to graph polygon rising at an angle in 3D space from the origin of the coordinate axes with shaded region on the $x$-$y$ plane?

I am trying to obtain a graph just like this one that visually shows that an objective function is maximised in z-direction at a certain point and where the “ground” of the graph is the $x$-$y$ ...
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### How to tumble a camera about a point

I'm trying to implement camera tumbling as described by this document. I have a camera that defines a view position and orientation. Additionally, there is a center of interest, which is a distance ...
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### How to represent 2D lines (i.e. on $x$ and $y-axis$) on a 3D graph using either Cartesian ($z=f(x,y)$) or Parametric $(x,y,z)=f(u,v)$

How to represent 2D lines (i.e. on $x$ and $y-axis$) on a 3D graph using either Cartesian ($z=f(x,y)$) or Parametric $(x,y,z)=f(u,v)$ Hi, I've been working on a Simplex problem and would like to ...