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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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What does $x= (0,0,0)$+$\lambda(-1,-1,-1)$ mean?

What does $x= (0,0,0)+\lambda(-1,-1,-1)$ mean? does it mean that the planes cross at the origin? Then what does $(-1,-1,-1)$ stand for?
Donna
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Why is the plane x=2/5 crossing the y-axis instead of the x-axis?

Why is the plane x=2/5 crossing the y-axis instead of the x-axis? I thought it would be opposite like when you graph a line. Would the vector be (.4,0,0)
Donna
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Maximum and minimum number of regions a line can pass in $xyz$ plane

Given any line in 3-space, what is the maximum and minimum number of regions that would it would pass through? Show how you know. I am lost with this question because I know that there are $8$ regions in the $xyz$ plane but don't know the maximum or…
Donna
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How many regions in 3D space?

If the axes of the xy-plane divide it into four regions (called quadrants), how many regions do the axes of the xyz-space divide it into? Explain your reasoning. I know it is 8, but can someone show me how it is 8? If I take a piece of paper and put…
Donna
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How many faces can have at most the intersection of two rectangular frustums?

In a 3D context, I want to evaluate the intersection of two rectangular frustums. The intersection of those two frustums will be a convex polytope, I think. What will be the maximum number of faces (and optionally, of vertices and edges) that can…
wip
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value of $d$ in $3$ dimensional Geometry

The point $P(1,2,3)$ is reflected in the $x-y$ plane, Then its image $Q$ is rotated by $180^\circ$ about the $x$ axis to produce $R$, finally $R$ is translated in the direction of positive $y$ axis through the distance $d$ to produce $S(1,3,3)$.…
DXT
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Condition for the generators through any one of the ends of an equi-conjugate diameter of the principal elliptic section of the hyperboloid

Question: Show that the generators through any one of the ends of an equi-conjugate diameter of the principal elliptic section of the hyperboloid $\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}{c^2} = 1$ are inclined to each other at an angle of $60…
Santosh
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3D objects in 2D drawing: How to get the size of a box relative to a known plane?

Sorry if this is a really badly worded question. Say you have a box of unknown size, and a planar object of a known size (say, a credit card). You arrange these object somehow (probably with the card aligned with two of the boxes axes) and take a…
J.Ashworth
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How to replicate 2-hand rotation like Tiltbrush?

So im trying to make a two-hand VR rotation mechanic, where the user grabs an object with one hand, and then with the other hand is able to rotate the object around a pivot point. That pivot point is gonna be a weighted point along the line between…
Jonas Mølgaard
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Formula for an Ellipsoid

Hi fellow mathematicians! I am having a hard time figuring out how an ellipsoid is globally defined. I know that a local formula for an ellipsoid is: $(\frac{x}{A})^2 + (\frac{y}{B})^2 + (\frac{z}{C})^2 - 1 = 0$. However, with this formula I can…
Leta
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Geometric mean of areas of tetrahedron

Consider a tetrahedron ABCD such that the areas of the triangles ABC, BCD, ACD, ABD are $k,l,m,n$ respectively. The volume of tetrahedron is $(1/6)$ cubic units . If each face ACB, ACD, BCD of the tetrahedron subtends a right angle at C, then we…
Koolman
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What is the closest point to a plane?

I can't solve this question: Let $\mathcal{P}$ be the plane containing the points $(-3,4,-2)$, $(1,4,0)$, and $(3,2,-1)$. Find the point in this plane that is closest to $(0,3,-1)$. I don't know how to do this question. Any hints/solutions? If it is…
user406996
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Find the points of contact of the tangent planes to the conicoid 2x^2-25y^2+2z^2=1.

Find the points of contact of the tangent planes to the conicoid 2x^2-25y^2+2z^2=1 which pass through the line joining the points (-12,1,12) and (13,-1,-13).I can't understand the meaning of this question ,plese somebody help me to understand this.…
Saroj Ghosh
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line through origin meets two lines at $P$ and $Q,$ then $(PQ)^2$

A line from the origin meet the lines $\displaystyle \frac{x-2}{1} = \frac{y-1}{-2} = \frac{z+1}{1}$ and $\displaystyle \frac{x-\frac{8}{3}}{2} = \frac{y+3}{-1}=\frac{z-1}{1}$ at points $P$ and $Q$ respectively, then $(PQ)^2$ is Attempt: assuming…
DXT
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Haversine formula that includes an altitude parameter?

I have this Python function that computes the great-circle distance between two points, but I want to modify it so that a third parameter, altitude, can be incorporated into the Haversine formula. from math import cos, sin, atan2, radians, sqrt def…
aweeeezy
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