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

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What order should I evaluate divergence and coordinate transformation if I want to use a different coordinate system?

I have a vector field in Cartesian coordinates. I need to find its divergence, but I need the divergence to be in spherical coordinates. However, the divergence of this field is far easier to ...
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3answers
43 views

Dividing line segments with ratios vs. fractions [on hold]

I know that $2:3$ is actually $\frac {2}{3}$. So when you split a line segment by a ratio, you would add $2$ and $3$ to get a fraction of $\frac {2}{5}$ that will be used to solve the problem. I ...
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17 views

How to calculate the coordinate of a point which depends on other points on a plane with specific distances

I have $8$ points on a plane $(x_1,y_1)....(x_8,y_8)$ among these $8$ points I know the coordinates for $7$ points and I have to find the $8^{th}$ point. Each points has the difference between all ...
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12 views

Coordinate geometry of circles; Circles through the points of intersection of 2 other circles

Here is my question. Let S=0 be the equation of circle 1 and T=0 be the equation of circle 2. There is a standard expression that, if you want the equation of a circle passing through the points of ...
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1answer
16 views

What is the basic idea of homogenisation of an equation?

I do get that when you are homogenising it makes it in an equation of pair of straight lines passing through origin but what is its actual point and its applications?
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1answer
22 views

Find the Equation of BC

$\Delta ABC$ with vertex $A(1,2)$ has equations of internal angle bisectors of $\angle B$ and $\angle C$ as $x-y-1=0$ and $2x+y-9=0$ Respectively. Find the Equation of $BC$ My approach: Solving for ...
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1answer
15 views

Coordinate Geometry of circles; Radical Axis question

If one of the diameters of the circle $x^2+y^2-2x-6y+6=0$ is a chord to the circle with center at $(2, 1)$, then the radius of the second circle is? Apparently the solution is $3$, with the ...
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19 views

Converting the coordinate system

I have the following mathematical relation: $[x,y,z]=k[u,v,f]$ where $k=function(u,f)$ x,y,z are the real world cartesian coordinates and u,v are its 2D projections in an image plane. f is a ...
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3answers
123 views

Find the point on the y-axis which is equidistant from the points $(6, 2)$ and $ (2, 10)$.

Find the point on the y-axis which is equidistant from the points $(6, 2) $ and $ (2, 10)$. Please help, there are no examples of this kind of sum in my book! I don't know how to solve it.
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2answers
19 views

Finding the vertices of a square - straight lines

Question: Each side of a square is of length $6$ units and the center of the square is $(-1, 2)$. One of its diagonals is parallel to $x + y = 0$. Find the co-ordinates of the vertices of the square. ...
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1answer
12 views

Coordinates rotation and function change

In the Cartesian coordinates $(x,y)$, I have a vector function $\bar{f}(x)=\hat{x}A\cos(yk)$, where $A$ and $k$ are constants. I make now a 45 degrees rotation (in the same plane) to the new set of ...
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1answer
22 views

How to find an equation of a plane perpendicular to two other planes and passing through a point

Please, could anybody help me with the next problem. I have two planes: $$ 2x-y+5z+3=0 \ (\text{red plane})\\ x+3y-z-7=0 \ (\text{green plane}) $$ And I need to find a plane which is perpendicular ...
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1answer
20 views

What basis and coordinate system is used in this quadratic Bézier triangle equation? $[x,y,z] = A*s^2 + B*t^2 + C*u^2 + D*2st + E*2tu + F*2su$

I have the following equation for a quadratic Bézier triangle, but I'm having a lot of trouble understanding how to describe it: $[x,y,z] = A*s^2 + B*t^2 + C*u^2 + D*2st + E*2tu + F*2su$ ...
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3answers
27 views

The sum of the squares of the length of the chord intercepted by the line x+y=n $n$…

Problem : The sum of the squares of the length of the chord intercepted by the line x+y=n $n \in N$ on the circle $x^2+y^2=4$ is (a) 11 (b) 22 (c) 33 (d) 13 I am unable to understand this ...
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1answer
21 views

Points defined by relations (an exercise from “System of Coordinates”)?

An exercise from "System of Coordinates" (by Gelfand, Glagoleva and Kirilov) asks me to "[t]ry to decide by yourself which sets of points are defined by these relations" and relations given are: a. ...
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1answer
49 views

Check if point lies on a line segment

I know there are shorter solutions that use dot product, but I don't know what the logic behind doing so involves so I came up with something that I understand myself (i will research the dot product ...
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2answers
35 views

Splitting a segment with a ratio

I came across the homework question that I attempted to do. After looking at the answers, and getting it wrong I didn't understand why. I'm specifically lost at why we would get a fraction of 2/5 ...
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1answer
18 views

A point P is selected inside an equilateral triangle. If sum of lengths of perpendicular dropped on to sides from P

Problem : A point P is selected inside an equilateral triangle. If sum of lengths of perpendicular dropped on to sides from P is 2014, then $\frac{\mathrm{length\; of \; altitude \; of \; ...
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1answer
22 views

Number of non zero integer values of $k$ for which the points ($k,k^2)$ lies inside the triangle formed by the given three lines

Problem : Number of non zero integer values of $k$ for which the points ($k,k^2)$ lies inside the triangle formed by the lines $11x+6y+14=0$, $9x+y-12=0$, $2x+5y-17=0$ (a) $0$ (b) $2$ (c) $3$ ...
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1answer
25 views

Family of lines $\sin\alpha x +\sin\beta y +\sin\gamma =0$

Problem : If $\sin(\alpha + \beta)\sin(\alpha -\beta) =\sin\gamma (2\sin\beta +\sin\gamma), 0 < \alpha , \beta ,\gamma <\pi$ then the family of lines $\sin\alpha x +\sin\beta y +\sin\gamma =0$ ...
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2answers
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If the circle $x^2+y^2+4x+22y+c=0$ bisects the circmuference of the circle $x^2+y^2-2x+8y-d=0$ the…

Problem : If the circle $x^2+y^2+4x+22y+c=0$ bisects the circmuference of the circle $x^2+y^2-2x+8y-d=0$ then c +d equals (a) 60 (b) 50 (c) 40 (d) 30 Solution : Equation of common chord ...
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1answer
28 views

Find if a rectangle passes through another in cartesian plane

I want to know how to prove or find out if the red big rectangle passes through one of these small rectangles i have the coordinates of the big rectangle (the top left) and i have it's width and ...
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1answer
209 views

How to show that a line pass through a point?

How to show that a line pass through a point? Two fixed straight line $OX$ and $OY$ are cut by a variable line at the points $A$ and $B$ respectively and $P$ and $Q$ are the feet of the ...
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1answer
70 views

What percentage of rooms would be trapped in the cube?

In the movie Cube the design is based heavily in math. I'm trying to figure out the approximate percentage of rooms that would be trapped. His knowledge of the outer shell's size allows Leaven to ...
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0answers
33 views

What distinguishes elliptical coordinates from polar coordinates?

I am trying to identify what characteristic distinguishes elliptical coordinates from polar coordinates. For concreteness, let's write down the expressions. Polar: $$ x=r \cos(t) \\ y=r \sin(t) $$ ...
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3answers
2k views

Minimum moves to reach destination [closed]

Given that a person is standing at $(0,0)$ and initially look in direction of $X$-axis. Now he can walk only at right angle to previous move. Like if he has to go to $(3,3)$ then $6$ moves are ...
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1answer
15 views

If the distances from origin of centre of three circles $x^2+y^2+2\lambda_i-c^2=0$ (i=1,2,3) are in G.P…

Problem : If the distances from origin of centre of three circles $x^2+y^2+2\lambda_i-c^2=0$ (i=1,2,3) are in G.P ( Geometric progression). Then lengths of tangents drawn to them from any point on the ...
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2answers
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Position of a point with respect to two reference frames

I working on a project where doing some image processing detect objects using Kinect camera and then move it to a desired location with a help of robotic arm. In this project the sensor gives pixel ...
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2answers
33 views

Partial differentiation in transformed coordinates

Following lecture notes from MIT it says that, given some variable $A = A(x, y, z(x, y, r, t), t)$ where $r$ is a transformed vertical coordinate $\left. \frac{\partial A}{\partial x} \right|_r = ...
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1answer
221 views

Intersection of two lines

What is the suggested method to find the intersection of two line *segments in 3D space programmatically? I mean there are various methods to solve a set of 2 linear equations, eg. Using ...
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1answer
38 views

Dot product in Curvilinear Coordinate Systems

I came across the dot product in polar, cylindrical, and spherical coordinates, today. After checking they were equivalent to the Cartesian versions, I started wondering how one would figure them out ...
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2answers
52 views

Better way to denote position on a sphere's surface

TL;DR: Read the bold text. If you have a rectangular plane, you can use two coordinates (X, Y) to define any position on the plane. If you have a sphere, you can still use polar coordinates to denote ...
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1answer
40 views

Sending Messages

N animals are sitting on the X axis and want to send messages to each other.One animal can send a message to another one if the distance between them is less or equal to K.P pairs of animals are ...
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Getting coordinate vector in linear algebra

I know how to get the coordinate vector of single matrices by just joining them and doing a gauss jordan. But these are a 2x2, I don't know how to go about this, apparently no elimination can take ...
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How many kinds of simple coordinates are there in a 2D space?

The question comes form an idea to solve a motion-with-potential problem in 1D space by finding a mathematically equivalent uniform-motion problem in 2D space. ...
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27 views

How do points change in a curved surface?

In the middle picture it shows a row of sticks at certain points along a flat surface. Now in the outer left picture (never-mind the outer right one), when the surface becomes curved the points ...
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2answers
35 views

Converting from set of Cartesian equations to Polar Equation

Is it possible to convert the set of Cartesian equations: $$x(t) = (20-30)*\cos(2t)+45*\cos(2t*(20-30)/20))$$ $$y(t) = (20-30)*\sin(2t)+45*\sin(2t*(20-30)/20))$$ where $$t \in [0,2\pi)$$ Into a ...
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3answers
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If there are $N$ people on the positive $x$-axis and one man can send a message to another one only if the distance between them is $\leq k $.

The question is how to determine a function which would decide if a pair of persons can communicate with each other, where communication is possible only if the distance between two individuals are ...
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1answer
38 views

Find coordinates for points on circle given R, 2 Points, and angle or 2 points and center?

I would like to find coordinates for points on a circle given: Radius of circle Coordinates of 2 points on the circle Angle of point 1, center, and point 2. Ultimately, I would like to write a ...
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2answers
41 views

Locating a point on a circle

I am having trouble getting the $(x,y)$ of a certain point on the circle. Please look at the image: The circles are the identical, the radius is $1000 \text{ units}$, $S$ is the center with ...
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1answer
362 views

How to calculate the coordinates of orthocentre.!!

How to calculate the coordinates of orthocentre.!! I was surfing through the net and got this formula.. $$x-\rm coordinate= \frac{x_1\tan A+x_2\tan B+x_3\tan C}{\tan A+\tan B+\tan C}$$ ...
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1answer
29 views

cylindrical and rectangular coordinates

Hi! I am currently working on some online homework and I don't understand what I am doing wrong when solving this problem. I know that the first and third coordinates are correct, but I seem to be ...
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Vocabulary of line coordinates

We can represent a line in 2 and 3 dimensions using 2 and 4 parameters respectively. For example, in 2 dimensions, we can represent a line using the angle $\theta$ of the normal and orthogonal offset ...
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1answer
119 views

Using paraboloidal coordinates

I have the 3-dimensional paraboloidal coordinates $$s_{\pm}=\sqrt{x^2+y^2+z^2}\pm z$$ $$\phi=ArcTan(y/x)$$ with the inverse transformation $$x=\sqrt{s_+ \cdot s_-}\cdot cos(\phi)$$ $$y=\sqrt{s_+ ...
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Calculating slope of 2 points 0n Earth (using longitude and latitude)?

How can I calculate the slope between 2 points on Earth using longitude and latitude of those two points? I need it to find the angle between two slopes.
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1answer
20 views

Estimate Rotation and Translation from two sets of points in different coordinate systems

I got one set of 3d $(x,y,z)$ points $( \# \geq3 )$ located in two diffent coordinatesystems. Is it possible to estimate the rotation and translation between these systems? Something like $$ ...
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1answer
162 views

Connection between covariant derivative and basis vectors.

I read here, Curvilinear page 11, that $$\frac{\partial}{\partial x^i}e_j=\Gamma^k_{ij}e_k$$ where the $e_i$'s are basis vectors. There seems to be some connection, but when I calculate it, for ...
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1answer
25 views

How many lines are larger lines made of in a dotted grid?

In a dotted 2d grid, lines can be drawn between the dots. But every dot that the line touches breaks the line up into smaller lines. I want to be able to work out how many lines this bigger line is ...
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1answer
26 views

Equation of pair of reflected straight lines given the equation of pair of incident straight lines

If $ax^2 + 2bxy + by^2 = 0$ represents a pair of lines, then find the combined equation of lines that can be obtained by reflecting these lines about the x-axis. I know that this can be done by ...
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27 views

Dividing an infinite plane into regions

I am currently working on a computer program for computing layout of graph-based diagrams. Their content is placed in an "infinite" 2D plane with cartesian coordinates in the center of the diagram. ...