Mathematics Stack Exchange
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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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Find the nearest set of points in 3d space

I have a set of 4 cuboids which are defined by 8 coordinates. The cuboids are grouped as follows (front view) Front view of cuboids So, each of these cuboids has coordinates as shown in the table below: Coordinates Basically, I want to be able to…
user2329142
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What does (plane) + (lambda*plane) refer to?

If $ax + by + cz + d = 0$ is Plane $1$ and $a'x + b'y + c'z + d' = 0$ is Plane $2$, then what does (Plane $1$) + $\lambda$(Plane $2$) signify? I got this doubt when the equation of a line was given as an intersection of two planes Plane $1$ and…
Krishan Sai
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3D Plane in a discrete domain.

I have a 3D plane defined by 3 floating points. I determine the plane equation parameters (ax+by+cz+d=0). I want to test all integer points (x,y,z) of the domain if them are in the plane. I have to verify the equation ax+by+cz+d=0. But because…
Luis Gonçalves
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Angle between two lines is $π/3$ where direction cosines are given

I have the following question before me: Let $l$, $m$ &$n$ be the direction cosines of two lines given by equations $l+m+n=0$. $fmn+gln+hlm=0$. I have to prove that for the angle between the two lines to be $π/3$, the following condition is…
HARVEER RAWAT
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If the mirror image of $P(a,6,9)$ with respect to line $\frac{x-3}{7} =\frac{y-2}{5}=\frac{z-1}{-9}$..

If the mirror image of $P(a,6,9)$ with respect to line $\frac{x-3}{7} =\frac{y-2}{5}=\frac{z-1}{-9}$ is $(20,b,-a-9)$, then find $|a+b|$ The general point of the line is $(3+7k,2+5k,1-9k)$ The direction ratio line joining this point to P…
Aditya
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Converting a 3D point (x,y,z) into a 2D point (x,y)

I am currently trying to export out a series of points (x,y,z) that my software has identified on a 3D model into a report. The thing is, I would also like to impose these 3-dimensional points onto a 2D image of the 3D model on the report. Is there…
Kelvin Lim
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Find the plane containing line $\frac{x-3}{2} = \frac{y+2}{2} =\frac{z-1}{3}$ and also contains its projection on the plane $2x+3y-z=5$

I am not really able to understand the question. I didn’t get the part ‘contains the projection of the line on the plane....’ How can a plane contain the projection of a line on another plane? Wouldn’t that just mean that required plane is…
Aditya
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How to find midpoint of an Arc on a 3D Plane

I'm not sure if this is even possible but here it goes: Let's assume we have a 3D Circle with 2 points on it A (1, 5, 2) B (5, 2, 1), and the circle's center O (0, 0, 0) Is it possible to find C based on the conditions that the distance from C to…
Hawaiian Pizza
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3D lines equation corresponding to the plane x+y+z=3

Perpendicular are drawn from the point on the line $\frac{{x + 2}}{2} = \frac{{y + 1}}{{ - 1}} = \frac{z}{3}$ to the plane $x+y+z=3$. Then the foot of the perpendicular lies on the line (A) $\frac{x}{5} = \frac{{y - 1}}{8} = \frac{{z -…
Samar Imam Zaidi
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Inequality that discribe Half space in front of space

The inequality that discribes the Half space of set of points in front of $yz$ plane is What i try:: The inequality that discribe the Half space of set of points is $$x\geq 0$$. Please tell me is i am right or wrong. If wrong plesse tell me…
jacky
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Equation of plane equidistant from 2 3d lines

The equation of the plane which is equidistant from lines $\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{3}$ and $\frac{x-2}{3}=\frac{y-3}{1}=\frac{z-1}{2}$ is Ax + By + Cz – 9 = 0 then A + B + C = ________. I used the concept of parametric points as…
Samar Imam Zaidi
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Plane containing projection of a line on another plane

The plane containing the line $\frac{x-3}{2}= \frac{y+2}{-1}=\frac{z-1}{3}$ and also containing its projection on the plane $2x + 3y – z = 5$, contains which one of the following points? $(A) (2, 2, 0) (B) (–2, 2, 2) (C) (0, –2, 2) (D) (2, 0,…
aarbee
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I want to do a mathematical derivation for 3D trilateration. I was trying to solve it as a system of equations but I am stuck.

I have 3 Anchor points $A1(x_1,y_1,z_1)$ , $A2(x_2,y_2,z_2)$, $A3(x_3,y_3,z_3)$ and we have to find the coordinates of $T(x,y,z)$. I know the distance of $T$ from each anchor point. How do I solve this problem?
Vishvachi Sinha
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Find if a 3D line segment intersects a closed 3D object (like a cube or sphere or random mesh)

As the question suggests, I would like to know how to find where a 3D line segment given by two points in 3D space would intersect another 3D object (formed by a collection of vertices, or their respective volume equations). My goal with this…
Microbob
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Finding the locus of planes by given conditions

There is point (1,2,3) on a line,then how to find the locus of all planes which are at a distance of 4 units from the point? I thought the shifting of origin will help. But how to proceed further??
Adas Hoper
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