Questions on coordinate systems, a geometric method where a point in n-dimensions is assigned a corresponding n-tuple of numbers.

learn more… | top users | synonyms

0
votes
0answers
23 views

Cylindrical coordinates: Paradox?

Let's say the vector field $\vec A_1 = \begin{pmatrix} r\\ 0 \\ z\end{pmatrix}$ in cylindrical coordinates is given and I want to calculate $\vec A_1 \cdot \vec e_r$, where $\vec e_r = \begin{pmatrix} ...
0
votes
0answers
17 views

Transforming a vector field in cylindrical coordinates - simple

I want to transform $\vec F = \alpha \vec r$ in cylindrical coordinates, i.e. $x=\rho \cos(\phi), y=\rho \sin(\phi), z=z$ Now since $\vec r = \begin{pmatrix} x \\ y \\ z\end{pmatrix}$ I receive $ ...
0
votes
0answers
21 views

How to formulate a coordinate transformation

Thank you in advance for taking the time to consider this. I'm trying to figure out how to formulate a coordinate transformation problem (at least that is what I think it is). Background: I have an ...
0
votes
0answers
13 views

Transform to cylindrical coordinate system

I tried so many approaches , at least give me a hint on how to find The unit vectors $$ \vec{V} = y\vec{i} + x\vec{j} + \frac{x^2}{\sqrt[2]{x^2+y^2})} \vec{k}\ $$
0
votes
0answers
19 views

Syncronize positions of 2 rectangles with different origin point while rotation

Suppose we have 2 rectangles in Cartesian coordinate system with (0,0) at the top left corner of the screen. Both of rectangles (a and ...
0
votes
0answers
135 views

Can someone help me convert definitions of hip movement in Cartesian coordinates into spherical coordinates?

I am a biomechanist. I am having a problem converting an idea in Cartesian coordinates $(x,y,z)$ to spherical coordinates $(r,\theta,\phi)$. I wondered if someone could help me. I can physically ...
0
votes
0answers
17 views

Polar-Cartesian Plot Interconversion

The Question How can we interconvert any general graph of polar or cartesian function so they give the same plot in the other coordinate system. Note: I do not mean to ask about interconverting a ...
0
votes
0answers
35 views

Coordinates of third vertex of right angled triangle in 3D

I am looking for a solution of the problem given at: How to find the third coordinate of a right triangle given 2 coordinates and lengths of each side but in 3D. Any help, please?
0
votes
1answer
19 views

What symmetry statement can be made about the points $(a, b)$ and $(b, a)$?

The question is: if $a$ and $b$ are any two numbers, what symmetry statement can be made about the points $(a, b)$ and $(b, a)$? I'm not sure whether this is a symmetry statements and whether it is ...
0
votes
4answers
48 views

Find a point on the line through $A=(2,3)$ and $B=(-5,-4)$ that is twice as far from $A$ as from $B$

Find a point on the line through $A=(2,3)$ and $B=(-5,-4)$ that is twice as far from $A$ as from $B$. Please indicate the actual position of the point.
1
vote
1answer
46 views

Equilateral triangular grid generation algorithm

In a research that I'm doing I need to generate an equilateral triangular grid and use this grid to mesh a region of space represented as a polygon to solve a PDE on this mesh. The problem is I need ...
1
vote
1answer
103 views

Calculating the angular velocity from x, y coordinate data

I have some video footage where I'm tracking insects over several hundred to thousand frames, resulting in a list of x, y coordinates for where the insect has been. I've found it pretty ...
5
votes
3answers
133 views

If ABCD is a square with A (0,0), C (2,2). If M is the mid point of AB and P is a variable point of CB, find the smallest value of DP+PM.

I assumed the coordinates of P = (h,2) to get the value of DP+PM= $\sqrt { (h-2)^2 +4}+\sqrt{h^2+1}$. Then I differentiated the equation wrt to h to get: $h(\sqrt{h^2+1}) -2\sqrt{h^2+1}+ ...
0
votes
0answers
4 views

How do i draw a circular polygon with angles and distances

My input data has 360 entries each corresponding to a angle, something like this 0° -2 1° -2.2 2° -2.1 3° -2.3 ... Each entry shows the distance from the center ...
0
votes
0answers
19 views

A function defined on a cylindrical surface, shift in x direction, and expansion in cylindrical coordinate system

A function is defined on a cylindrical surface ($r=r_0$), $\psi_1(r,\phi,z)=f(z)cos(m\phi)\delta(r-r_0)$, where m is a integer, can be 1,2,3..;$r,\phi,z$ are coordinate system variable. If $\psi$ ...
0
votes
1answer
19 views

Method in calculating distance from a point ta a line in 3D rectangle coordinate system

I have a problem while trying to calculating the distance form point $B(0,3,4)$ to the y-axis in xyz coordinate system. Here is how I calculate it: There is point $Y(0,t,0)$ belonging to the y-axis ...
0
votes
0answers
17 views

Finding coordinate axis vectors to yield a specific transformation

For a project I am working on, I will be given a point $\textbf{a}$ in a global 3-D coordinate system, as well as a point $\textbf{a}^\prime$ in a local coordinate system. (The global coordinate ...
0
votes
1answer
27 views

Which Points are not Contained in the Line

The Circle $$x^2+y^2-4x=0$$ is cut by a line $AB$ at two points. If $A$,$B$ and two other points $C(1,0)$ and $D(0,1)$ are Concyclic, Then which of the Following points are not contained by the line. ...
0
votes
0answers
16 views

Transform Confocal Ellipsodal to Spherical Coordinates

I heard that someone published a paper showing that the confocal ellipsoidal coordinate system can transform into the spherical coordinates under special limit evaluations, however I was unable to ...
0
votes
2answers
16 views

Question regarding vectors within a circle in an $x$- and $y$-plane.

In an $x$ and $y$ coordinate plane, with respect to the points $A, B$, and $C$ on a circle of radius $1$, find the minimum value of $\vec {AB} \cdot \vec {AC}$ So far, taking $O$ as the origin I've ...
0
votes
1answer
26 views

Writing same equation in different forms

I am working with a unit circle with imaginary integration. I know from experience that this can be written as $f(\theta)=\cos t+ i \sin t$ or $e^{i \theta } $ My question would be if i have a circle ...
1
vote
1answer
20 views

Proving that $2$-D parabolic coordinates are orthogonal

How can we prove that the parabolic coordinate system in two dimensions is orthogonal? I tried using the dot product, but don't know where to start or what basis vectors can be used in two dimensions. ...
0
votes
0answers
10 views

Show the equation for the length of a path on the surface of a sphere.

Here is my problem. What I am confused about is going from cartesian to spherical coordinates. I do know that L= integral from point $1$ to point $2$ of $(\sqrt{(dx^2+dy^2)})$. (in cartesian ...
0
votes
0answers
24 views

Coordinates in file isn't in the range -180 to 180 respective -90 to 90?

Hello! I'm creating an android version of a PC program (I've contacted the complany who owns the PC program, so it's legal). The program is in the core a GPS, but is used to navigate pre-defined ...
0
votes
1answer
39 views

coordinate transformation and tensor

A 2 dimensional Euclidean space is represented by two different coordinate systems: the Cartesian system $(x_1,x_2)$ and an alternative system $(\xi^1,\xi^2)$ where ...
0
votes
1answer
20 views

Integral in Spherical and Rectangular Coordinates

If I'm evaluating $\int^b_a r dz$, where $r$ is a variable in spherical coordinates and $z$ is a variable in rectangular coordinates, do I need to transform $dz$ in spherical coordinates? If so, how ...
0
votes
1answer
146 views

Z coordinates of 3rd point (vertex) of a right triangle given all data in 3D

this is my first post.. I hope this good I have 1 triangle in space (3D)... and I know all data except the coordinates of 3er point(vertex)... for example this: then: ...
0
votes
0answers
12 views

how to visualize this statement: Matrix M falls in a Ball-set.

So the question is simple: Assume you are told that a matrix M has the following property: $\|M\|_2<1$, i.e. it falls in unitary ball. When we say it is inside a ball set, if you imagine a ...
2
votes
1answer
264 views

What is the difference between coordinates transformation and change of coordinates?

In the context on 3D computer graphics, what is the difference between coordinates transformation and change of coordinates? It can just be a matter of notation, but my book makes a clear distinction ...
0
votes
4answers
62 views

Equation of circle touching a parabola

Suppose we have a parabola $y^2=4x$ . Now, how to write equation of circle touching parabola at $(4,4)$ and passing thru focus? I know that for this parabola focus will lie at $(1,0)$ so we may ...
2
votes
1answer
54 views

If $x=\pi a y^{1/2}$ then why is $\frac{\partial^n}{\partial x^n}=-2\left(\frac{y^{3/2}}{\pi a}\right)^n \frac{\partial^n}{\partial y^n}$?

While I was reading this question, I was surprised that the transformation of a 'simple' differential operator $\displaystyle \frac{\partial^n}{\partial x^n}$ by substituting $x=\pi a y^{\frac{1}{2}} ...
6
votes
0answers
133 views

Physical components of a third-order tensor

Aris' book Vectors, Tensors, and the Basic Equations of Fluid Mechanics describes how to convert between covariant, contravariant, and physical components of vectors and tensors. For example, in ...
1
vote
3answers
115 views

What Vector Operation Performs $(a,b)*(c,d)=(ac-bd,ad+bc)$?

When you multiply two complex numbers, you get \begin{equation} (a+bi)\times(c+di)=(ac-bd)+(ad+bc)i \end{equation} As betterexplained.com points out, this multiplication of two complex numbers can be ...
1
vote
1answer
28 views

Point coordinates at a fixed distance from a vector

I would like to solve the following generic problem by using vector notation that I will use it to improve my algorithm. I have a vector P1P2 that points P1 and P2 are known. Furthermore, an ...
0
votes
1answer
25 views

Cartesian to spherical coordinate system

Hey I want to convert Cartesian to spherical coordinate system. I referred many site and for calculating elevation angle $\theta$ from positive z axis they all used formula $\arctan \frac { ...
0
votes
0answers
32 views

Locus of the Orthocentre of a triangle.

Vertices of a variable triangle are $(3,4),(5\cosθ,5\sinθ)$ and $(5\sinθ,−5\cosθ)$ , where $θ∈R$. Locus of its orthocentre is. A. $x^2+y^2+6x+8y−25=0$ B. $x^2+y^2−6x−8y+25=0$ C. ...
0
votes
2answers
563 views

Finding two vertices of a rectangle given two vertices and angle?

I have a rectangle where I know the coordinates of the opposite diagonal corners. I also know the angle that the rectangle is rotated. I would like to solve to find the coordinates of the other two ...
1
vote
2answers
51 views

How to determine the distance to one point from another in a 3D coordinate system?

I wonder how I can calculate the distance between two coordinates in a $3D$ coordinate-system. Like this. I've read about the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ (How) Can ...
0
votes
2answers
68 views

Coordinate geometry reflection of point

I have point in $1st$ octant($ x, y, z$ all positive). Now I take the mirror image of that point about $xy$ plane. I guess that new point will be simple $ (x, y ,-z)$. Verify if I am right. Further ...
13
votes
1answer
730 views

Conditions for two straight lines to intersect: is this exam question wrong?

I am pretty sure this question (from a university admission test exam) is wrong. Two lines: $a_1x+b_1y+c_1=0$, $a_2x+b_2y+c_2=0$, intersect only if (a) $a_1a_2-b_1b_2=0\;\;\;$ (b) ...
0
votes
2answers
28 views

Show that both the given lines are parellel (3-D)

Guys I am trying to solve the problem below which I found in a book: Show that the lines $\frac{x-1}{2}=\frac{2-y}{1}=\frac{5-z}{1}$ and $\frac{4-x}{4}=\frac{3+y}{2}=\frac{5+z}{2}$ are parallel. ...
2
votes
0answers
84 views

Problem regarding the speed of two points $A$ and $B$ moving with constant speed in the plane [duplicate]

Consider a Point A that moves linearly on the positive x-axis with the speed 1 m/s and another Point B at a distance L from A with position (L,0). With each forward motion of point A the Point B moves ...
2
votes
3answers
51 views

How to determine the equation and length of this curve consistently formed by the intersection of Circles

Consider a Point $A$ that moves linearly on the positive $x$-axis with the velocity $1$ m/s and another Point $B$ at a distance $L$ from $A$ with position $(L,0)$. With each forward motion of point ...
3
votes
2answers
68 views

Is there a structure similar to a graph but which includes a sense of direction, like north, west, east, south?

I understand that graphs do not have any notion of "facing", that is, a sense of relative or cardinal directions. Using a conventional graph, it's not possible to say "go left at vertex A," as far as ...
0
votes
1answer
99 views

Determining third vertex of the right angled isosceles triangle

If A(9,-9), B(1,-3) are the vertices of a right angled isosceles triangle, then the third vertex is?? Here in this question i got stuck to the point that which side is taken as the given coordinates. ...
1
vote
1answer
29 views

Given two points, I need to find all of the 'sections' of the graph that the line segment travels through.

What do I mean by "sections"? Imagine a piece of graph paper. Each square bounded by integer horizontal and vertical grid lines is a "section", and is named after its lower left coordinate — (1,1), ...
3
votes
3answers
273 views

3D coordinates of circle center given three point on the circle.

Given the three coordinates $(x_1, y_1, z_1)$, $(x_2, y_2, z_2)$, $(x_3, y_3, z_3)$ defining a circle in 3D space, how to find the coordinates of the center of the circle $(x_0, y_0, z_0)$?
0
votes
1answer
35 views

How to find the velocity and accelaration in a 3d space with 6 degrees of freedom?

I have the following rigid body: I assume that the body is a symmetric cylinder.x,y,z are the axes of the reference frame resulting from a transformation involving three orthogonal rotations ...
1
vote
1answer
30 views

Construct a procedure which determines the location of the shadow of a rectangluar box.

I drew a 3d rectangular box on a coordinate plan consisting of x, y, and z. A procedure is to be created that will determine the location of the shadow of the box on one of the coordinate planes. I ...
1
vote
1answer
33 views

Determining transformation matrix from six points

Given that I have the locations of three points: p1 = [1.0,1.0,1.0] p2 = [1.0,2.0,1.0] p3 = [1.0,1.0,2.0] ...and I know their transformed counterparts: ...