# 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.

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### Find coordinates of the center of the mass - line integral

Find the coordinates of the center of the mass of the curve $$x^2+y^2=1, x+2y+3z=12$$ I find calculating line integrals in 3D problematic and really don't know how to approach this one. I think ...
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### Find all values for a and b such that two vectors are not perpendicular

I'm stuck on this question that asks to find all values for a and b such that two vectors u = (-1, 2, a-2), and v = (b, 4, -2) are not perpendicular. I know that if the dot product of u.v = 0 then ...
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### 3D & Trigonometry: Rotating a Cube [closed]

I am programming a 3D game in a 2D environment, and I am trying to make a 3D cube. I did that, and I am trying to rotate said cube, so I can see all the sides of it. I found this lesson on Khan ...
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### Is there any other way to find the intersecting line between the following 2 planes?

Given a pyramid $T.ABCD$ where $ABCD$ is a square. See the following figure. $L$ and $K$ are midpoints of $TA$ and $TC$ respectively. The line intersecting plane $TBD$ and $BKL$ is need to draw. My ...
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### Does there exists 'Superhero' cuboids?

There exists heronian figures,i.e., the figures with integral area and perimeter. This also works for heronian 3D shapes, which have integral volume and integral surface area. Some figures, which are ...
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### Three Dimensional [closed]

Q. Find the equation of right circular cylinder of radius $2$ and whose axis is the straight line $\frac{x}{1}=\frac{y}{-2}=\frac{z}{2}$.
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### Component vectors from a 3D vector

If vector $v_{xy}$ is a vector on the $xy$ plane of magnitude $r$, and $v_{yz}$ is a vector on the $yz$ plane also of magnitude $r$, then $v_{xy} + v_{yx}$ results in vector $v$ of magnitude $R$. How,...
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### Finding The Volume Of a Shape That Is Given By the Formula $3x^2 + 2y^2 + z^2 \leq 6$

how can I find the volume of the shape that is given by the formula $3x^2 + 2y^2 + z^2 \leq 6$ ? Thanks!
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### How to find if a 3d point is in/on/outside of tetrahedron

How can I find if a 3d point is in/on/outside of tetrahedron defined by 3d coordinates (The point and the tetrahedron)? This is what I found on ethernet: You now just check if a point P is on the ...
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### Right circular cone shortest distance question from a junior high school st. [duplicate]

Ant's shortest distance that it can travel Can you show me the answer in the cone unfolded. I would be glad if you guys can show me the solution in a simple way because I am a high school student.
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### Intersection of oblate spheroid $\frac{x^2+y^2}{R_e^2}+\frac{z^2}{R_p^2} =1$ and plane $n_xx+n_yy+n_zz=0$

To calculate the distance between two points on Earth, I used 3 different approaches. For small distances, I used the Euclidean distance. For medium distances, I used the arc length on the circle ...
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### How do I implement a simulation of a damped 3 dimensional spherical wave in MATLAB?

From this link I was able to successfully implement a damped wave. I used MATLAB's movie command to send it frames (or snapshots) of the current values of the wave over time. Here is the MATLAB ...
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### Finding fraction of a volume by visualization of cube being cut into separate pieces

Cube $ABCDEFGH$ is cut into four pieces by cutting along planes $BCHE$ and $BDHF.$ Find the fraction of the volume occupied by the piece containing the vertex $A.$ I'm not really able to visualize ...
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### Euler's Formula and Existence of Solids

Euler's formula tells us that the number of vertices, edges and faces of a 3D solid have to satisfy the relationship $V+F=E+2$. How about the converse, if I have a triple of numbers that fulfill this ...
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### Find the area of the cone part [closed]

Find the area of the cone $z=\sqrt{x^2+y^2}$ when $-1<x+y<5$ and $-3<-x+y<3$
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### Find the total area of ​the pyramid.

The base of a pyramid is an isosceles trapezoid whose parallel sides are equal to $a$ and $b\; (a> b).$ Each side face is oblique to the base making an angle $\alpha$. Find the total area of ​​the ...
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### Consider a cube whose faces are given and a triangle whose vertices given then the number of point of intersection of cube and triangle is

Consider a cube whose faces are given by $x+y+z=3\sqrt{3}$, $x+y+z=2\sqrt{3}$, $4x-5y+z=\sqrt{42}$, $4x-5y+z=2\sqrt{42}$, $2x+y-3z=\sqrt{14}$, $2x+y-3z=2\sqrt{14}$, and a triangle ...
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### PDE $u_{x} ^{2} +u_{y}^{2}+u_{z}^{2}=1$ with constant data on plane

$$u_{x} ^{2} +u_{y}^{2}+u_{z}^{2}=1, \qquad u=k \;\text{ on the plane }\; \alpha x+\beta y + z =0, \text{ }$$ where $k$, $\alpha$ and $\beta$ are constants I've been trying to solve this PDE ...
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### Given $|\vec a| = 3, |\vec b| = 5$ and $|\vec a+\vec b| = 7$. Determine $|\vec a-\vec b|$.

I can't seem to understand this question at all. It does not make sense to me. The question is Given $\left|\vec a\right| = 3, \left|\vec b\right| = 5$ and $\left|\vec a+\vec b\right| = 7$. ...
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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 = ________....
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### Calculating coefficients for least squares [cross-posted from CrossValidated]

In this blog, this author says to calculate the coefficients for the equation $$Flat(x, y) = A + Bx + Cy + Dx^2 + Ey^2 + Fxy$$ using least squares. I found this PDF that shows how to do the ...
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### How do I find the outward unit vectors which are normal to the surface of the sphere at the intersection points of the ray and the sphere?

Consider the surface of the sphere given by the equation $$(x − 3)^2 + (y − 4)^2 + z^2 = 25.$$ You shoot a ray from the point $(8, 4, 0)$ along the vector $v = \langle1, 0, 1\rangle$. What are the ...
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### Is there a mathematical model to work out which face of a dice will appear when you turn it

I written a program to draw a 3D cube [a dice]. And I hard coded which face appears when you move it from one face to another. So imagine I start with a 1 facing me; I have a 5 above, a 4 to the right,...
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### 3d Camera View Volume

Suppose I have 80x80x80 cube with the center point located at (0,0,0) as the condition drawn below: : I want to convert this parallel projection view volume into a canonical view volume. I have ...
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### How to handle degenerate case for interpolating with 3 point plane

There's a task to approximate 4th point located inside of triangle of 3 points. 3 points, each with coordinates $[x, y, z]$ - find value for the 4th point $z$ coordinate - given its $[x, y]$ ...
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### What's the high school definition of 2 perpendicular lines in 3D space in the UK and the US?

In my country, 2 lines in 3D space are said to be perpendicular if the angle between them is 90 degrees, and the angle between 2 lines in space are said to be the (either right or acute) angle of 2 ...
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### The surface area of the pyramid [closed]

What is the surface area of ​​the regular triangular pyramid if the base edge is $a = 12$ cm and height $H = 8$ cm?
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### Is there a rotation matrix that can invert any 3D vector? [closed]

For example, could a single rotation matrix convert the following vectors: vec{1, 1, 1} to vec{-1, -1, -1} ...
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### Let $\ell$ be the line parametrized as $(t, 2t+1, 3t+2)$ and let $P$ be the plane with equation $x+y+z = 1$.

Let $\ell$ be the line parametrized as $(t, 2t+1, 3t+2)$ and let $P$ be the plane with equation $x+y+z = 1$. This question has been asked but the answers there don't help me and I am still unsure of ...
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### Can Cavalieri's Principle be applied to a Pyramid and a Cylinder?

I know that Cavalieri's Principle makes it so that if two prisms/cylinders, or two pyramids/cones have the same area at a cross section parallel to the base, and they have the same height, they also ...
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### Removing the rotational component in optical flow

I am working on a basic self driving algorithm using a monocular image sequence. For this, the optical flow between every two frames based on tracked keypoints is calculated (which is a vector for ...
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### How many planes can two three-dimensional vectors fill in the three-dimensional space?

In the "Introduction to linear algebra", G. Strang gives an example of two 3d vectors (say v=[1,0,0] and w= [0,2,3] ) and says that combinations of cv + dw fill a plane in R3. I read that the 3d ...
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### Compound angles formula derivation(crown molding)

So I've been trying to get my head around this for a week now. It's a practical problem, but the geometry seems more involved then I initially thought. When you want to attach a crown molding to a ...
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### Function from $\mathbb{R}^3 \rightarrow \mathbb{R}$ with “nice looking” isosurfaces

I am looking for a function $f: \mathbb{R}^3 \rightarrow \mathbb{R}$ with a rather particular requirement. For the purpose of rendering with the Marching Cubes algorithm, I would like $f$ to have ...
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### Finding Arc Lengths in a 3D cartesian coordinate system from any 2 arbitrary points

So I'm familiar with the parametric form of the arc length integral that follows a given path at any point $t$, but what do you do when you have a 3D equation that does not follow any specific path $t$...
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### Parametrizing the surface $z=7-x^2-4y^2$

I am willing to parameterize the surface formed by paraboloid $z=7-x^2-4y^2$ bounded below by the plane $z=3$. i know its simple that parameterize is $x=u$, $y=v$ and $z=7-u^2-4v^2$ But i am unable to ...
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### find the angle between 2 points in space and the line vertical to one of them.

I wanted to calculate the angle between 2 points in space and the line, which is vertical to one of them. for example, we got p1(x1,y1,z1) and p2(x2,y2,z2) and a line which is parallel to z axis and ...
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### Cutting cylinder with the plane

How to find the equation of the surface obtained by cutting the cylinder $x^2+y^2=9$ with the plane $x-y+z=4$ I know that it should be an ellipse . what i have done is i have eliminated $x$ from both ...
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### Rotation of a Plane in 3d about a line [closed]

I have a set of points in the XY planes, I want to translate them all to the YZ plane by rotating about a line. Basically, Here, in this cube Imagine I have a list of points on 2376 plane, I want to ...
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### A sphere cuts the coordinate axes at points P,Q,R and also passes through the origin. Then which of the equations is satisfied?

A variable plane passes through a fixed point $(a,b,c)$ and cuts the coordinate axes at $P,Q,R$. Then the coordinates of the centre of the sphere passing through$P,Q,R$ and the origin satisfies the ...
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### Volume of the solid above the parabolic cylinder $z=1-y^2$

Find the volume of the solid bounded above by the Parabolic cylinder $z=1-y^2$ and below the plane $2x+3y+z+10=0$ and on the sides of circular cylinder $x^2+y^2-x=0$ Since this is region obtained by ...
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### Finding plane which cuts prism in a section which forms an equilateral triangle

We are given a rectangular prism having $x+y=0,x-y=0$ and $x=1$ as its faces. We have to find the normal vector to the plane which cuts this prism in a section that forms an equilateral triangle. Now ...
Parametric Equation I have 2 parametric equation, $$(100\sin(t),100\cos(t),2t^2+200)$$ and, $$(100\cos(s), 100\sin(s), 2s^2+160)$$ How do I find the interception of these two parametric equations. I ...
### There exists an infinite set $S\subset \mathbb R^3$ such that any $3$ vectors in $S$ are linearly independent.
There exists an infinite set $S\subset \mathbb R^3$ such that any $3$ vectors in $S$ are linearly independent. Start with a basis $\beta=\{v_1,v_2,v_3\}$.Take a vector not in any coordinate plane,...