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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Construct 3D plane from 2 points and minimize angle of two vectors with its normal

I have as input two points $P, Q \in E^3$ and two vectors $\vec{v}_1, \vec{v}_2 \in R^3$. I need to construct a plane $(\vec{n}, d)$ such that the two points are in the plane and the angles between ...
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1answer
28 views

Show right angles for orthogonal vectors in 3D

This question is one of simple computational geometry, similar to what I posted in http://stackoverflow.com/questions/34186711/rgl-vector-diagrams-show-right-angles-for-orthogonal-vectors. But no one ...
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24 views

3D graphics: Sphere intersection occlusion

Suppose I have two solid spheres $s_1$ and $s_2$ (and by solid spheres I mean 'balls' in the strict mathematical sense). We know their centres and radii, and we know that they have some overlapping ...
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1answer
18 views

Given a start point in 3d and a quaternion and length to Point B can you find Point B

Let's assume I have a start point A (x, y, z). Now the object has moved and the new orientation is given by a quaternion Q and it's pointing at point B which is L length away from it. How can I ...
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1answer
145 views

Find points of Rectangle given two diagonal points and a normal in 3D

I'm developing a geometry framework in a program I'm working on that contains all the good stuff like vectors, points, lines, planes, polygons, etc. I was attempting to create a rectangle object, but ...
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1answer
25 views

What would be a description of this set in $\mathbb R^3$?

Suppose that $K=\{(x,y,z)\in \mathbb R^3|x\geq 0,y\geq 0, xy\geq z^2\}$. Let $K_0=\{x\in\mathbb R^3|\langle x,k\rangle\leq 0\forall k\in K\}$. What would be a description of the set $K_0$? I don't ...
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14 views

Finding equation of a plane normal to an intersection curve

The cone with equation $z^2=x^2+y^2$ and the plane with equation $2x+3y+4z=-2$ intersect in an ellipse. Find the equation of the plane normal to the ellipse at the point $P(3,4,-5)$. I try to find ...
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2answers
40 views

3D shape with orthogonal projections that form circles of the same radius.

Let's say you have a 3D shape. The side view, front view, and top view of the shape are all circles of the same radius. Does the shape have to be a sphere, or is it possible that it could be another ...
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16 views

Finding vector components and converting terminal point to cylindrical coordinates

Is my logic correct in finding the component form of vector v? The questions are below. For part a, since the vector is in the yz-plane, I wrote the vector as a 2D vector showing only the y and z ...
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1answer
29 views

$e^{-\frac{1}{x}}e^{-\frac{1}{1-x}}$ in 3D

I have the function $f(x) = e^{-\frac{1}{x}}e^{-\frac{1}{1-x}}$, which produces this graphic: What should $f(x,y)$ be to look like a 'hill', i.e. $f(x)$ spinned about vertical axis?
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1answer
93 views

Rotate points from one plane to another

I'm trying to create a algorithm that will rotate points given on plane 1 to plane 2. I have found two different ways of doing this. My question is ... Why are the transformation matrices different ...
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1answer
48 views

Is $M-{\hat v}^T \hat v$, positive definite (with M positive definite)?

Given a symmetric, positive definite matrix M in $\mathbb{R}^{3\times3}$, and a vector $v\in\mathbb{R}^3$. Let $\hat v$ be the skew-symmetric matrix associated with $v$: $\hat v = \begin{bmatrix} ...
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0answers
28 views

Rotating points from one plane to another plane

I'm trying to create a function that will rotate points given on plane 1 to plane 2. I have found two different ways of doing this. The attached spreadsheet shows the two different ways as Solution ...
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1answer
40 views

Compute the area defined by four non-planar points

Say we have 4 non-planar points in a 3D space (but preferably it should work in any dimension, so no cross products), $a,b,c,d$, and these points define a non-flat area. A point on that area may be ...
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11 views

aligning a matrix to reference matrix

Assuming X$_0$ as a matrix which represent some sort of transformation between TWO different coordinate system. Now, as a function of time the matrix which has three column vectors evolves in to X'. ...
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1answer
33 views

The line $\frac{x+6}{5}=\frac{y+10}{3}=\frac{z+14}{8}$ is the hypotenuse of an isosceles right angled triangle whose opposite vertex is $(7,2,4)$

The line $\dfrac{x+6}{5}=\dfrac{y+10}{3}=\dfrac{z+14}{8}$ is the hypotenuse of an isosceles right angled triangle whose opposite vertex is $(7,2,4)$.Find the equation of the remaining sides. My ...
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48 views

Prove that planes $AOA',BOB'$ and $COC'$ pass through the line $\frac{x}{l_1+l_2+l_3}=\frac{y}{m_1+m_2+m_3}=\frac{z}{n_1+n_2+n_3}$

$O$ is the origin and lines $OA,OB$ and $OC$ have direction cosines $l_1,m_1,n_1;l_2,m_2,n_2;l_3,m_3,n_3$ respectively.If lines $OA',OB'$ and $OC'$ bisect angles $BOC,COA$ and $AOB$,respectively,prove ...
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1answer
25 views

Minimal definition of a Platonic Solid

I searched in Google for the definition of Platonic solid, and I found: A platonic solid is a polyhedron all of whose faces are congruent regular polygons, and where the same number of faces ...
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1answer
27 views

If the projections of $OA$ and $OB$ on the plane $z=0$ make angles $\phi_1$ and $\phi_2$,respectively,with the $x-$axis

$OA,OB,OC,$ with $O$ as origin, are three mutually perpendicular lines whose direction cosines are $l_1,m_1,n_1;l_2,m_2,n_2$ and $l_3,m_3,n_3$ respectively. If the projections of $OA$ and $OB$ on the ...
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1answer
61 views

How to draw the 3d planes?

The equations for planes I have are $x=0$, $x=1$, $y=0$, $y=1$, $z=0$, $z=1$ but these to me look like equation of the lines. Apparently, they form a cube in 3d coordinates. Is it possible use some ...
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2answers
35 views

Prove that for all values of $\lambda$ and $\mu,$ the two planes intersect on the same line.

Prove that for all values of $\lambda$ and $\mu,$ the planes $\frac{2x}{a}+\frac{y}{b}+\frac{2z}{c}-1+\lambda(\frac{x}{a}-\frac{2y}{b}-\frac{z}{c}-2)=0$ and ...
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1answer
24 views

Show that there is a common line of intersection of the three given planes.

Let $x-y\sin\alpha-z\sin\beta=0,x\sin\alpha-y+z\sin\gamma=0$ and $x\sin\beta+y\sin\gamma-z=0$ be the equations of the planes such that $\alpha+\beta+\gamma=\frac{\pi}{2}$,(where ...
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1answer
42 views

The new position of $O,$ when triangle is rotated about side $AB$ by $90^\circ$ can be

Consider the triangle $AOB$ in the $xy$-plane where $A\equiv(1,0,0);B\equiv(0,2,0);$ and $O(0,0,0)$.The new position of $O,$ when triangle is rotated about side $AB$ by $90^\circ$ can be ...
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0answers
32 views

3d collsion rig math

I'm in quite the bind. The end result I'm looking for is to create a finger rig with collision detection. This will be done in a 3d app. The diagrams are acting as a basic visual display. B1 is ...
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1answer
30 views

Method of finding Arc length parameterization of a 3d curve

r(t) = cos^3 t i + sin^3 t j; 0 < t < pi/2. r'(t) = -3cos^2 t sin t + 3 sin^2 t cos t ||r'(t)|| = 3 sin t cos t Now to find the arc length parameterization, we need S = integration from t0 ...
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1answer
18 views

A parallelopiped is formed by planes drawn through the points $(1,2,3)$ and $(9,8,5)$ parallel to the coordinate planes

A parallelopiped is formed by planes drawn through the points $(1,2,3)$ and $(9,8,5)$ parallel to the coordinate planes then which of the following is not the length of an edge of this rectangular ...
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1answer
23 views

A rod of length $2$ units whose one end is $(1,0,-1)$ and the other end touches the plane $x-2y+2z+4=0$

A rod of length $2$ units whose one end is $(1,0,-1)$ and the other end touches the plane $x-2y+2z+4=0,$ then find the center of the region which the rod traces on the plane. The rod sweeps out the ...
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117 views

Find the equation of the plane which bisects that angle between the given planes which is acute and which contains the origin.

Consider the planes $3x-6y+2z+5=0$ and $4x-12y+3z=3$.Find the equation of the plane which bisects that angle between the given planes which is acute and which contains the origin. The two bisectors ...
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1answer
48 views

If the shortest distance between the skew lines $AB$ and $CD$ is $8$ ,find the volume of the tetrahedron.

Given a tetrahedron $ABCD$ with $D$ at the top and $AB=12,CD=6$.If the shortest distance between the skew lines $AB$ and $CD$ is $8$ and the angle between them is $\frac{\pi}{6}$,then find the volume ...
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1answer
26 views

Segments joining each vertex with the centroid of the opposite face are concurrent at the point $P$.Find the position vector of $P$

$OABC$ is a tetrahedron where $O$ is the origin.Position vectors of its angular points $A,B$ and $C$ are $\vec{a},\vec{b}$ and $\vec{c}$ respectively. Segments joining each vertex with the centroid of ...
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1answer
34 views

Prove that there are infinite planes containing both the lines $L_1,L_2$ and that there is a unique plane containing both the lines $L_3,L_4.$

Let $L_1:\frac{x-1}{1}=\frac{y-0}{1}=\frac{z-2}{-5}$ $L_2:\frac{x-2}{2}=\frac{y-1}{2}=\frac{z+3}{-10}$ and let $L_3:\frac{x-0}{-6}=\frac{y-1}{9}=\frac{z-0}{-3}$ ...
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2answers
49 views

Find the equation of the plane perpendicular to the plane $P$ and containing line $L_1$.

Consider a plane $P$ passing through $A(\lambda,3,\mu)$,$B(-1,3,2)$ and $C(7,5,10)$ and a straight line $L$ with positive direction cosines passing through $A$,bisecting $BC$ and makes equal angles ...
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If $P$ and $Q$ are points on two skew lines.If $P$ and $Q$ are nearest to each other.Find $\vec{OP},\vec{OQ}$

Let $P$ and $Q$ be points on the lines $L_1:\vec{r}=6\hat{i}+7\hat{j}+4\hat{k}+\lambda(3\hat{i}-1\hat{j}+\hat{k})$ and $L_2:\vec{r}=-9\hat{j}+2\hat{k}+\mu(-3\hat{i}+2\hat{j}+4\hat{k})$ respectively ...
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1answer
59 views

How to interpret a 3D plot

I am trying to interpret 3D plots but its driving me nuts. Lets say I want to see the relationship between 3 variables and I have data as following: ...
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2answers
43 views

Rotate around point whilst maintaining forward facing direction

I have a stationary point, the origin (O) at (0, 0, 0) and a moving Point (P) that I wish to have rotating around O with a fixed radius (d). However, rather than just rotating around I always want to ...
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0answers
20 views

Finding rotation and translation of a planar object in 3d

I have a planar object, say a polygon $A_1A_2\ldots A_n$ in the 3-dimensional Euclidean space. It is translated by a vector $v$ and rotated by a rotation matrix $R$, and the resulting image is ...
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1answer
75 views

Curl and Divergence definitions - Is this definition mathematically correct?

I've been using Stewart's Calculus: Early Transcendentals in my Calculus class, and one of the definitions of curl offered by the book was $$\text{curl } \vec F = \nabla\times \vec F$$ where ...
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1answer
196 views

Equations of the two lines through the origin which intersect the line $\frac{x-3}{2}=\frac{y-3}{1}=\frac{z}{1}$ at an angle of $\frac{\pi}{3}$

Find the equations of the two lines through the origin which intersect the line $\frac{x-3}{2}=\frac{y-3}{1}=\frac{z}{1}$ at an angle of $\frac{\pi}{3}$. Let the direction ratios of the two ...
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2answers
38 views

The equation of the plane which passes through the point of intersection of two space lines and at greatest distance from the point $(0,0,0)$

The equation of the plane which passes through the point of intersection of lines $\frac{x-1}{3}=\frac{y-2}{1}=\frac{z-3}{2}$ and $\frac{x-3}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ and at greatest distance ...
2
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1answer
39 views

The value of $m$ for which straight line $3x-2y+z+3=0=4x-3y+4z+1$ is parallel to the plane $2x-y+mz-2=0$ is

The value of $m$ for which straight line $3x-2y+z+3=0=4x-3y+4z+1$ is parallel to the plane $2x-y+mz-2=0$ is $(A)-2\hspace{1cm}(B)8\hspace{1cm}(C)-18\hspace{1cm}(D)11$ My Attempt:The plane ...
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11 views

relative sizes of noncoplanar objects

Say that there are two objects in the distance, one of a known size, the other of an unknown size. Both objects are two dimensional, and take the form of rectangles. They are not coplanar, but I know ...
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29 views

A 3D problem on the range of angles

$CD$, of length $14$ units, is a line fixed on the ground. $AB$ is a thin rod fixed in the air. A ring, which is attached to $AB$, can slide freely on $AB$. An elastic band (remaining taut all the ...
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1answer
26 views

Arc Length in 3D space

So given a function $$f(x,y)=x^3+30xy+2y^3,$$ I am able to find the maximum value in a specific region. However, I need to be able to calculate the distance that would be traversed by a particle ...
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1answer
57 views

3D coordinates rotation — new direction for Z axis

I need to rotate 3D coordinate system so Z axis points in new direction. So, I have a direction defined by spherical coordinates ($\theta$, $\phi$), where $\theta$ (in $[0, \pi]$ range) is polar and ...
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1answer
30 views

Finding 2 vectors in a circle in 3D space

I'm trying to find 2 vectors in a given circle (not a sphere). This circle can be at a random position, rotation. Given the position, rotation, and radius of the circle, where the center position of ...
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2answers
44 views

Given a line and a point in 3D, how to find the closest point on the line?

I have a point given by $P = (P_x, P_y, P_z)$, and a line give by the two points $Q = (Q_x, Q_y, Q_z)$ and $R = (R_x, R_y, R_z)$. I'd like to know a general formula to figure out the closest point to ...
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0answers
35 views

3d rotation of a triangle onto surface of sphere?

I'm trying to develop a 3D model of a sphere, and I want to place triangles near the surface, normalized to the surface at that point. I am having trouble with the mathematics of the rotation of the ...
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1answer
46 views

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 ...
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1answer
47 views

Equation of circle in 3d Plane?

Suppose I have a sphere centered at origin. $$ x^2+y^2+z^2=5 $$ and a plane $$ \vec{r}.(\hat{i}+\hat{j}+\hat{k})=3\sqrt{3} $$ And this plane cuts the sphere at a circular region. How do I write the ...
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1answer
31 views

Plotting a function in 3D (theory)

I made a program which draws/plots a function like it is given in the picture ...