# Tagged Questions

The (3d) tag is for things related to 3-dimensions. For geometry of 3-dimensional solids, please use instead (solid-geometry). For geometry that is not on a plane, but otherwise agnostic of dimensions, perhaps (euclidean-geometry) or (analytic-geometry) should also be considered.

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### Equation of a perpendicular plane without dot product

How can i find the equation of the plane that passes through $(6,4,-2)$ and is perpendicular to the line that passes through points $(1,4,-5)$ and $(7,-2,3)$ without dot product? I tried findind the ...
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### Parametric equations for a line perpendicular to two given lines.

We are given two lines in $\mathbb{R}^3$: $L1 : x = 4t , y = 1-2t , z = 2+2t;\\ L2 : x = 1+t , y = 1-t , z = -1+4t.$ The question asked was to find the parametric equations for the line that is ...
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### Find tangent common tangent plane…

Number of common tangent planes to the sphere $(x+2)^2 +y^2 +z^2 =1$ and $(x-2)^2 +y^2 +z^2 =1$ that pass through origin.
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### Find volume of cube with the help of eqn of plane

The volume of cube whose two faces lie on the plane 6x-3y+2z+1=0 and 6x-3y+2z+4=0?
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### Find a point 90° left or right from a point (x,y,z) in a 3D space.

How can I find a point which is 90° left or right from a point (x,y,z) in a 3D space? for example if I have the point $(x,y,z)$ how to find $(x1,y1,z1)$ and $(x2,y2,z2)$.
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### Tricubic Interpolation

I am currently writing a plugin for 3D analysis software and I am working with a data grid where certain values are stored at XYZ coordinates, and I need to find an estimated value of a point that ...
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### how to find the pivot/axis and angle that move one coordinates space to another?

I am writing a plugin for a 3d modeler, and I am stuck. For my plugin, I need to get the axis and the angle used for rotating a 3d object. But I only get the coordinates (~ 3dmatrices) of the objects ...
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### Removing Discontinuity in 3-space without changing the partial derivative

Is it possible to find a version of the function $$f(x,y) = x\cdot \lfloor y \rfloor + \lfloor x\rfloor^2$$ That is continuous. ANY operation is allowed in changing the function as long as the ...
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### Is there some relationship for all points on a rectangle?

For a line in 3D space, you can know that for each P on the line with endpoints A and B and length L, it holds that ||P-A|| + ||P-B|| = L My question is: is there a similar expression for points on ...
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### Perform a rotation in 3D world

I got a character at some point $A$ facing to point $O$ that is equal to $(0,0,0)$, then I move it to point $B$ and I want to rotate him to face point $O$. Since this is 3D world I think that I need ...
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### Slicing a 3d surface using a 2d line equation

So what I'm trying to do is to find the equation of a 2d function on a 3d surface using a 2d line equation. With : $z = f(x, y)$ the equation of the surface and $ax + by + c = 0$ the line ...
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### Progressively embed ( = superscribe?) and immerse …

$\mathbb R^1$ is superscribed/embedded on $\mathbb R^2$ and $\mathbb R^2$ in turn immersed in $\mathbb R 3$. Graph of a line $x(u,v), y(u,v), z(u,v),f(u,v)=0$ is superscribed or embedded on ...
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### Euler angle to direction vector which is right?

I tried to implement a first person shooter camera using Euler angles with the order pitch-->yaw rotation.(pitch is rotate round X axis, yaw is rotate round Y axis) Many tutorial gave the formula ...
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### Geometric Optimization

In 1990 W. Kuperberg conjectured that it is impossible to have seven infinite mutually disjoint unit cylinders all touching a unit sphere. As a first step towards a solution I would like to answer the ...
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### Does 3D euclidean space allows vector sum in 2 dimensions?

Is this right to add two orthogonal vectors to to get one vector, using this vector in calculations and after getting results, decomposing result vector to get orthogonal components? I am a programmer,...
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### Angle between planes challenging Question

The plane $r.(a,3,5)=10$ is inclined at an angle of $45^\circ$ to the plane $r.(-5,1,4)$ Find the value(s) of $a$ up to $2$ decimal places. I attempted this problem by forming an equation where I ...
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### How to programmatically find dodecahedron's edges as couple of vertices

I'm a newbie here, and I'm not a mathematician, so I hope you could help me. Online I found that the 20 vertex of a dodecahedron can be easily expressed as: ...
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### Finding the radius of a sphere inscribed in a right prism

We have right prism $ABCA_{1}B_{1}C_{1}$ and points $E$, $D$ such that: $A_{1}E:EB_{1}=B_{1}D:DC_{1}=1:2$ The distance between lines $AE$ and $BD$ is $\sqrt{13}$. Find the radius ...
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### Trigonometric Word Problem in 3D

The question I am having trouble on is as follows: "As an Expert Mathematics Witness, you have been presented with a Ballistics Report, and a Police Report as your evidence. Use the information ...
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### Calculating cosine of dihedral angle

Let $O,A,B,C$ be points in space such that $\angle AOB=60^{\circ},\angle BOC=90^{\circ},\angle COA=120^{\circ}$ Let $\theta$ be the acute angle between the planes $AOB$ and $AOC$. Find $\cos\theta.$ ...
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### How to calculate rotation quaternion between two orientation quaternions?

I have some device (3D pointer) connected to my computer which returns it's position (in cartesian XYZ system) and orientation (in quaternions). I receive this values about 30 times/sec. Now I need ...
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### What is the formula for a cone built from two arbitrary vectors?

Suppose there is an arbitrary vector in 3D space : $\vec v = (a,b,c)$ , starting from point $(x_0,y_0,z_0)$ which is the center or 'spine' of the cone. There is also the vector $\vec u = (h,i,j)$ , ...
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### Calculate a normal to vector lying on a plane formed by $2$ vectors

Let's presume I have two vectors $V_1$ and $V_2$. As far as I understand normal to a vector is all vectors lying on a plane perpendicular to it. What I need is a normal to $V_1$ that lies on a plane ...
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### Converting a 3D line's equation into vector form.

How exactly can I convert the below equation into the vector form? (i.e. V(i,j,k) form or $a*i+b*j+c*k$ form): $$\frac{x-5}{-10}=\frac{y-3}{-6}=\frac{z-2}{-4}$$ I'm actually trying to find the angle ...
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### Find cone-plane intersection points in a construction

I have two points on the X axis, A and B, which are connected to the two points, C and D on the sketch plane parallel to XY plane. I have a point E which lies at distance h from D point in Y direction ...
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### Transformation of 3D vectors to other planes in 3D

Suppose I have a set of points A, B, C, D, E, F... defined by the 3D vectors AB, AC, AD, AE, AF, AG etc. I can describe the geometry of these by defining them in an arbitrary plane e.g. z = 0 ...
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### Determine plane rotation in 3D when only knowing the length of it sides?

For an assignment in computer graphics, i need to be able to determine a plane's rotation by just holding it in front of my webcam. So basically I only got 2D coords of the plane's points. I searched ...
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### Confusion in Total faces in Cone: 3D

I have checked in many places about how many faces does a Cone have.. As per this link. There is 1 face in Cone As per this link, there are 2 faces in cone As per this Video, A Cone has one face ...
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### Finding extremas of a function

$f(x,y) = xe^{-{x^3}+{y^3}}$ and I am to find extrema values of that 2-variable function. I come up with the point $P(3^{1/3},0,f(3^{1/3},0))$ is its only critical point. I tried to apply second ...
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### Quaternion angle - Opengl rendering

I have been using a 6dof LSM6DS0 IMU unit (with accelerometer and gyroscope). I am trying to calculate the angle of rotation around all the three axes and Render a 3D cube using opengl to immitate the ...
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### Calculate 2D into 3D coordinates by given edge-points of Polygon

im drawing an image with a orthogonal projection matrix and need to calculate a 2D Point back into its 3D Point. I have a Polygon and i know its 3D-World and 2D-Screen edge coordinates. Now i want to ...
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### How to understand rotation around a point VS rotation of axes?

I am puzzled about linear transformation and coordinate transformation, any help will be appreciated. From wiki rotation matrix, we know rotates points in the xy-Cartesian plane counter-clockwise ...
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### Convert direction vector to euler angles

How do I convert a direction vector to euler angles? I need to change the position of a character's head in a Java program that I'm writing. The pose of the head uses euler angles. I know the ...
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### Sketching the surface $z=\frac{x^2y}{3}$

I am trying to sketch the part of $x^2+y^2=9$ which lies in the first octant between the surfaces $z=0$ and $z=\frac{x^2y}{3}$. I understand that $x^2+y^2=9$ is a cylinder with radius three, ...
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### 3D bend equation derivation.

This is how the bend work: (The number is the angle) I was searching for an equation to bend an object in a specific axis and I found one,It worked pretty well,but unfortunately I don't know why it ...
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### How to determine what kind of curve in 3d geometry

I am having difficulty in determining type of given curve in 3d geometry.Is there any test in which I can differentiate between 1) Circle 2) Cone 3) Cylinder 4) Circle When equation of 3d curve ...
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### Rotating one 3d-vector to another only by using rotations about the coordinate axes.

If I have a vector v=(x,y,z) and would like to transform another vector u by using only rotations about the coordinate axes to be in the direction of v, how can I find required angles and the order of ...
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### Shortest Distance between planes

This is a question which puzzled our entire math class including our teacher, I'm referring to part (b), we're fine with part (a). We don't understand the reason for taking the dot product and the ...
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### find the length of the path traversed by a particle

Let the position of a particle in three dimensional space at time t be (t, cos t, sin t). Then the length of the path traversed by the particle between the times t = 0 and t = 2π by my approach i'm ...
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### Difference between a Möbius Strip and a Simple Surface

I am trying to distinguish between a Möbius strip and a surface that has no separations, holes and a connected boundary (homeomorphic to a disk or a half-sphere). Since a Möbius strip also has all the ...
I am trying to transform the following integral to an integral in cartesian coordinates. $$\int^{2\pi}_0\int^1_0\int^{\sqrt{1-r^2}}_0r \ dzdrd\theta$$ I cannot really visualise how the region enclosed ...