Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [3d]

For things related to 3 dimensions. For geometry of 3-dimensional solids, please use instead (solid-geometry). For non-planar geometry, but otherwise agnostic of dimensions, perhaps (euclidean-geometry) or (analytic-geometry) should also be considered.

This tag is for things related to 3-dimensions. For geometry of 3-dimensional solids, please use instead . For non-planar geometry, but otherwise agnostic of dimensions, perhaps or should also be considered.

Learn more about 3-dimensional space here.

3724 questions
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Volume of tetrahedron detected by four planes in $\mathbb R^3$

Given the equation of $4$ planes in $\mathbb R^3$, find the volume of the tetrahedron. The planes are: $$\begin{align}&P1: x+3y+z=2\\&P2: x-2y+z=2\\&P3: -x+z=4\\&P4: x=3\end{align}$$ I dont even know where to start. I thought there was going to be a…
Julian Navarro
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How to get the equation for a 3D line given 2 angles

Given 2 angles (a1, a2), where a1 is the horizontal angle and a2 is the vertical, how can I use these two angles to get the equation/s of a line that passes through the origin. ex: 0° x 0° / 180° x 0° = (x,y,z) (0,(-∞,∞),0)
Luke Wright
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A site gives $x^2 - y^2$ for a hyperboloid-lie 3d graph, what about z? Is there a name for this 3d graph?

A site https://www.math3d.org/ renders this 3d graph as its homepage and gives this formula for that graph $x^2 - y^2$ What about z? What is the full formula for that graph? Is there a name for this 3d graph?
JakeMZ
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2 answers

Ratio of volume of Tetrahedron

If $A,B,C,D$ are $4$ coplanar points and $A',B',C',D'$ are their projections on any plane. If $\alpha$ is the angle between plane of $ABCD$ and the plane of projections. Then the ratio of volume of volume of Tetrahedron $AB'C'D'$ to volume of…
jacky
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Why the intercept form and normal form is not applicable in 3d space?

Today one of my folks told me during studying 3d geometry that the intercept form and normal form are not applicable in the 3d space where in 2d they both hold good 1.intercept form: x/a + y/b =1 2. Normal form : xcos(a)+ ysin(a) =p
Vishal Kumar
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Circles in different Dimensions in the $X-Y-Z$ Plane.

Explain the difference in the graphs of $(x – 1)^2 + (y + 3)^2 = 4$ and $(x – 1)^2 + (z + 3)^2 = 4$, both in the $(x,y,z)$-space.
Donna
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What do these programming formulas for 3D coordinate processing implement?

I am studying a C++ program related to 3D coordinates and can not understand what two formulas implemented are doing so I need help in understanding the meaning of the lines (indicated below) for (int i = 5; i<= 95; i++){ float depth = sqrt…
user1420
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Foot of perpendicular in 3 dimensions

Let us suppose that $Q$ is a foot of perpendicular from a point $P (2,4,3) $on the line joining the points $A(1,2,4)$ and $B(3,4,5)$; then what are the coordinates of $Q$? My try: Had this been a two dimensional problem, I would have found the…
Zlatan
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from m$^3$ to length, width, height of cube

Is it possible to calculate the length, width, height of a cube, based on just the m$^3$. For example if I have a cube with sides of $5$ meters: the m$^3$ is $125$ m$^3$. Is it possible to go back from $125$ m$^3$ to the sizes of the $3$ dimensions…
guest
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1 answer

Get range of 3D object given lowest and highest point and angle

How do you get 3D range of object (highlighted in red below) given its lowest (PL) and highest (PH) (x,y,z) coordinates and orientation of object? Image below is a top view of a box.
tjvg1991
  • 356
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3-Dimentional array

I'm good in 2-D array which is the regular array that has rows and columns, but I have to deal with the 3D array and I can't imagine it, I tried searching for it but with no clue. Any big example of 3D array? Anything through it make it clear for…
lel
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2 answers

Rotation of plane about a line

The plane denoted by $$P_1 : 4x + 7y + 4z + 81 = 0$$ is rotated through a right angle about its line of intersection with the plane $$P_2 : 5x + 3y + 10z = 25$$. If the plane in its new position be denoted by $P$, and the distance of this plane from…
Koolman
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1 answer

Ratio of coordinate

In the above question, how have they written the ratio given in the first step of solution?
a25bedc5-3d09-41b8-82fb-ea6c353d75ae
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How are 3d images rendered in 2d space?

There was a similar question asked on this same site a few years ago (How to transform a set of 3D vectors into a 2D plane, from a view point of another 3D vector?), but the answerer seemed to kind of jump into hard-to-follow math steps without an…
moonman239
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Equation of a sphere

How to find the equation of a sphere which has got the intersection of another given sphere with a given plane as its great circle? I am not able to find the equation of circle of intersection of the given sphere and plane.
HARVEER RAWAT
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