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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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Prove that the direction ratios of the line of intersection of two planes $\vec r\cdot(a\hat i+ b\hat j+ c\hat k)=m $ and...

Prove that the direction ratios of the line of intersection of two planes $\vec r\cdot(a\hat i+ b\hat j+ c\hat k)=m $ and $\vec r\cdot(d\hat i+ e\hat j+ f\hat k)=n$ is given by $\begin{vmatrix}\hat i&\hat j&\hat k\\a&b&c\\d&e&f\end{vmatrix}$ where…
Tatai
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Plane of given tetrahedral region

Let $T$ be the tetrahedral region given by vertices at $(1, 0, 0)$, $(0, 0, −1)$, $(−2, 0, 0)$, and $(−1, −1, −1)$. Compute the volume of this tetrahedron using triple integrals My progress: I have trouble on evaluating the plane for which this…
rentbuyer
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Use pythagoras in a cuboid to find x.

my daughter has a question and I am lost how to solve it. I have a rectangular box with the following dimensions (see below picture) Height: $2x-1$ Width: $x+8$ Length: $2x+4$ the line running across the rectangle from bottom left corner to top…
kurasa
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shortest distance b/w 2 lines

I have 2 Question on $3-D$ Geometry (1) The point on the Line $\displaystyle \frac{x-3}{1}=\frac{y-5}{-2}=\frac{z-7}{1}$ which is Nearest to the Line $\displaystyle \frac{x+1}{7}=\frac{y+1}{6}=\frac{z+1}{1}$ is (2) If a Plane Contain $3-$ Lines…
juantheron
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Expression of the Equations of 3D Egg Shape in terms of degrees

I'd basically like to have 3D version of this article section or this section. So for my case, there are two angles for latitude and longitude to construct 3D egg. Any hint to extend the formula to 3D would be appreciated.
Tae-Sung Shin
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Simplest way to determine if two 3D boxes intersect?

Given If given two sets of two points in 3D space (where they are defined to be the corners of the box): Box1: P1 = (961.46, 215.15, 1465.44) P2 = (970.02, 214.93, 1481.77) Translational Matrix for Box 1: Box2: P1 = (1093.52, -499.50, 896.11) P2 =…
Eric F
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Intersection of a line segment and a paraboloid in 3D

Suppose I have a line segment $L$ in 3D: $$x=a_1(1-t)+b_1t$$ $$y=a_2(1-t)+b_2t$$ $$z=(a_1^2+a_2^2-k_1^2)(1-t)+(b_1^2+b_2^2-k_2^2)t$$ Because $L$ is line segment then $0\leq t\leq 1$. And defining paraboloid $P$ in 3D: $$P:z=2x^2+2y^2-1$$ Where…
kotoll
  • 281
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Lines and angles in 3D space

If given the angles between 3 intersecting lines (ie $A, B, C$ pass through $O$, and $\angle AB \angle AC \angle BC$ are given) how can you find the angle between one line and the plane created by the other two lines
Martin Welsh
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Area of a triangle inside a prism

The question goes as follows. Consider $3$ planes $$1)2x+y+z=3$$ $$2)x-y+2z=4$$ $$3)x+y=2$$ such that they don't intersect in a single line and form a prism.Another plane $4)$ is made through some point $P$ on line of intersection of…
Navin
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Groups of coplanar points on tetrahedron

The points $P_1, P_2, \dots, P_{10}$ are either vertices or midpoints of edges of a tetrahedron. For $1 < i < j < k \le 10$, how many groups of four coplanar points $(P_1, P_i, P_j, P_k)$ exist? (Where $P_1$ is a vertex.) The number of points which…
Koolman
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What is the equation of a 3D cone with generalised tilt?

What is the equation of a 3D cone with generalized tilt? I've noticed that in most equations given to represent a cone, there is no parameter which defines the tilt of the cone in 3D space and that most of them have their point at the origin…
Charlene
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Conclusion that can be drawn from 4 points in space whose angles are $90^{\circ}$

Four points A, B, C and D are in space such that angles $A\hat BC, B\hat CD, C\hat DA$ and $D\hat AB$ are all right angles, then A, B, C, D cannot be coplanar A, B, C, D are necessarily coplanar. A, B, C, D may or may not be coplanar. No such…
Dhanush Krishna
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How to find the best-fit transformation between two sets of 3D observations

Let us assume that I have two sets of observations, A and B. Each of them is a list of 3D points. They describe the same set of world 3D points at the same order. However, they are given in different coordiante systems (so that they might be…
user288134
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What makes the inside of a shape the inside?

A question occurred to me when browsing SE this evening, just curious. What specifies the inside of a 3D construct? If I have a hollow sphere, what's to say that the world isn't the inside, and the center of the sphere isn't the outside. Picture the…
Sam Weaver
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points of intersection on a randomly situated plane and ellipsoid (spherical) in 3d space

if i have an ellipsoid and a plane oriented in any way in a 3 dimensional coordinate system, and they intersect; is there a way to find an equation that describes (or at least approximates) all points of intersection for example, an ellipsoid that…
mayotic
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