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.

learn more… | top users | synonyms

0
votes
2answers
25 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 ...
0
votes
0answers
14 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 ...
1
vote
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?
0
votes
1answer
46 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 ...
0
votes
1answer
47 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} ...
0
votes
0answers
16 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 ...
1
vote
1answer
33 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 ...
0
votes
0answers
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'. ...
2
votes
1answer
31 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 ...
2
votes
0answers
46 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 ...
1
vote
1answer
20 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 ...
1
vote
1answer
26 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 ...
1
vote
1answer
35 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 ...
1
vote
2answers
33 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 ...
2
votes
1answer
22 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 ...
0
votes
1answer
37 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 ...
0
votes
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 ...
0
votes
1answer
19 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 ...
0
votes
1answer
17 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 ...
0
votes
1answer
21 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 ...
0
votes
0answers
53 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 ...
1
vote
1answer
43 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 ...
0
votes
1answer
23 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 ...
0
votes
1answer
30 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 $L_3:\frac{x-0}{-6}=\frac{y-1}{9}=\frac{z-0}{-3}$ ...
0
votes
2answers
21 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 ...
1
vote
0answers
18 views

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 ...
1
vote
1answer
52 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: ...
1
vote
2answers
38 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 ...
1
vote
0answers
17 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 ...
4
votes
1answer
69 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 ...
0
votes
1answer
96 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 ...
0
votes
2answers
30 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
votes
1answer
33 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 ...
1
vote
0answers
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 ...
1
vote
0answers
28 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 ...
0
votes
1answer
24 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 ...
0
votes
1answer
45 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 ...
2
votes
1answer
25 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 ...
0
votes
2answers
35 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 ...
0
votes
0answers
21 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 ...
0
votes
1answer
38 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 ...
0
votes
1answer
35 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 ...
0
votes
1answer
30 views

Plotting a function in 3D (theory)

I made a program which draws/plots a function like it is given in the picture ...
4
votes
0answers
36 views

Decomposing geodesic tessellations over a sphere into parallelograms

I'm working with some icosahedron-based tessellations of triangles over the surface of a sphere. Class I and Class II tessellations have a nice property where, cutting along the edges of the ...
0
votes
0answers
6 views

Kelvin problem with restriction to only one type of polyhedron

If we only allow one type of polyhedron, what would be the answer to the Kelvin problem? Would the Kelvin conjecture be true?
1
vote
1answer
26 views

Why must the outside limits of an iterated be constant?

My book claims that in an iterated integral $$\int_a^b \int_{g(x)}^{h(x)} f(x, y) \, dy \, dx$$ $h$ and $j$ are allowed to be any functions of $x$ not containing $y$, but $a$ and $b$ must be constant ...
1
vote
0answers
12 views

Limits of integration of a multivariable function?

My book is filled with problems such as $\int_{1}^{x} f(x, y) dy$ . My question is if there is a good reason why the top limit of integration is an $x$. When we integrate the function with respect to ...
0
votes
1answer
23 views

How to obtain 3D coordinates of the point by the length of the vector?

How can I obtain R3 position of a point? For example, I've got two points linked by a vector: p1 = (-4000;250;-5000) p2 = (428;776;-300) |v| = 6926.32 I'd like to find a point which lies on the line ...
0
votes
0answers
53 views

Drunk tankist problem

Imagine that we have a military tank. At time t0, we get an initial rotation matrix M0, that specify the initial position of the tank acording to world's frame F0. At time t0 we also have an initial ...
0
votes
1answer
18 views

What is the purpose of $v$ in the parametric equation for a sphere?

The longitude / latitude parameterization of a sphere is described by: $x = cos(φ) * cos(θ) \quad y = cos(φ) * sin(θ) \quad z = sin(φ)\quad$ where $\quadθ = 2 π u$ and $φ = π v - π / 2$ I ...