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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1answer
525 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
369 views

Given 2 points/coordinates, how do I express in $ax + by + c = 0$ form?

Given 2 points eg. $(x_1, y_1), (x_2, y_2)$ how do I express in $ax + by + c$ form? I am supposed to find the intersection of 2 lines. I have 2 points for 1 line, and the other line will be ...
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1answer
140 views

locus difficult

A fixed point is at a perpendicular distance a from a fixed straight line and a point moves so that is distance from the fixed point is always equal to its distance from the fixed line.Find the ...
2
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1answer
188 views

Find the locus of the point which divides segment AB internally in the ratio 1:2.

A and B are variable points on X and Y axis respectively,such that l(ab)=4.Find the locus of the point which divides segment AB internally in the ratio 1:2. I think that it must be a circle . or ...
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1answer
126 views

Cylindrical coordinate system

Let us consider a fixed reference point P and another point Q in space. Suppose you want to express the position of Q with respect to P in cylindrical coordinate system. Now in the cylindrical ...
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0answers
100 views

Parameterizing a spherical cap in cylindrical coordinates

In calculating the mean curvature for a surface of the form $(f(z)\cos(\theta), f(z)\sin(\theta), z)$ I need to use some checks to ensure I haven't made any mistakes along the way. The one I would ...
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1answer
144 views

Are cartesian coordinates “more fundamental” than other coordinates, and are they inherently tied to $\mathbb R^n$?

Are the Cartesian coordinates more "fundamental" than other coordinate systems? When someone says $\mathbb R^n$ do we implicitly mean the set of points PLUS Cartesian coordinate system? Sometimes I ...
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1answer
36 views

coordinate of shorter line

If I have a line segment with endpoints AB,CD. The length of the line is 5 units. If I make the line shorter (eg. 3 units), and one of the endpoints is still AB, how do I figure out what the new CD ...
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53 views

Geometry finding area problem

A regular 2N -sided polygon of perimeter L has its vertices lying on a circle. Find the radius of the circle and the area of the polygon.
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1answer
109 views

Calculate the X,Y values of an ellipse

I guess am confused somewhere. I have the length(l) and breadth(b) of an ellipse enclosing rectangle. I know the center point and the angle(x) that the line makes with the center. I want to know the ...
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0answers
82 views

Changing coordinate system with non standard definitions

The standard coordinate transformation to polar coordinates is $$ \begin{cases} x=r\cos(\varphi)\\ y=r\sin(\varphi) \end{cases} $$ with $r\in[0,\infty), \ \varphi\in[0,2\pi)$ The question is whether I ...
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2answers
1k 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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0answers
4k views

Converting an equation from cartesian to cylindrical coordinates

This is going to seem pretty basic, but I'm trying to figure out if there is a problem in my homework's text or if it's just not clicking for me. I have to find the volume for the paraboloid $$z = 6 ...
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3answers
80 views

How to find the integral by changing the coordinates?

Let R be the region in the first quadrant where $$3 \geq y-x \geq 0$$ $$5 \geq xy \geq2$$ Compute $$\int_A (x^2-y^2)\,dx\,dy.$$ I tried to use $ u= y-x, v= xy$ as my change of coordinates, but then I ...
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1answer
617 views

How to determine gradient of vector in cylindrical coordinates?

I am wondering how to actually determine the gradient of a vector in cylindrical coordinates. I have seen a lot of websites that just say what the general form is but I cannot seem to understand how ...
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1answer
254 views

Are spherical coordinates unique orthogonal coordinates on sphere?

Spherical coordinates on unit sphere are defined by the following transformation: $$\begin{cases}x=\sin\theta\cos\varphi\\ y=\sin\theta\sin\varphi\\ z=\cos\theta\end{cases}$$ Are these coordinates ...
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1answer
224 views

sketching regions of three variables

If i had a solid region, V, such that $x^2+y^2+z^2\le9$, $x^2+y^2\le4$, $x\le0$ and $z\ge1$ what would be the easiest method to sketch this region? Can someone run me through steps as how to tackle ...
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1answer
3k views

Calculate Camera Pitch & Yaw To Face Point

How do you calculate pitch & yaw for a camera so that it faces a certain 3D point? Variables Camera X, Y, Z Point X, Y, Z Current Half Solution Currently I know how to calculate the pitch, ...
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1answer
45 views

Algorithm to approximate the closest nonlinear formula(funciton) for an arbitrary set of points?

I have a table which concists of XY points (so I have a set of points hehe), where X represents the Velocity and Y the Real World Speed. Those points are not linear. With two points it's easy to ...
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2answers
2k views

Finding a line perpendicular to a line and passing through the intersection of other two lines

So here is the question as in my text book Find the equation of the line through the intersection of $2x - 3y + 4 = 0 $ and $3x + 4y - 5 = 0$ and perpendicular to $6x - 7y + c = 0$ so I ...
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1answer
67 views

Center of Distance

I am given $N$ points in a 2D plane($x$ and $y$ coordinates). I have to find a point in this plane with coordinates $X$ and $Y$ such that: $$\sum_{i=1}^N \max\{|X - A_i|, |Y - B_i|\}\text{ is ...
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1answer
351 views

Which matrix transforms my vector field $F(r,\theta,\phi)$ from cylindrical to spherical coordinates

I am looking for the matrix that I have to apply my vector at the position $(r,\theta, z)$ to in order to get the appropriate vector in spherical coordinates. I am totally okay, if you could give me ...
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2answers
353 views

How to calculate the number of integral points inside an area

How many integral solutions (x, y) exist satisfying the equation |y| + |x| ≤ 4 My approach: I have made the graph after opening the the modulus in the above equation by making four equations. Now ...
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1answer
383 views

Get 2D direction vector from 1D rotation (for game development)

I am working on a game where my object is supposed to move forward based on it's rotation (the direction it's facing) I tried this: increase object x to cos(rotation) increase object y to ...
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1answer
1k views

Express spherical coordinates with different centers in terms of each other.

Imagine that you have two spheres with a distance $R$ from one center to the other one. Now, it is well known how one would get the cartesian position vector of each point in sphere 1 by using ...
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1answer
68 views

The smallest value of $|a|$ such that the lines $ x = a+m $, $y = -2 $ and $y = mx$ are concurrent

Question If the line $ x = a+m $, $y = -2 $ and $y = mx$ are concurrent, the least value of $|a|$ is (A) $\sqrt{2}$ (B) $2\sqrt{2}$ (C) $2\sqrt{3}$ (D) $3\sqrt{2}$ Solution Since the ...
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0answers
100 views

coordinate transformation and scaling

I have a global coordinate system that I need to transform to a local coordinate system. The new and old coordinate systems are shown below. Using transformation rules, I came with with the ...
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0answers
57 views

What's the mathematical formulation for frames for reference?

In this lecture I've come across an interesting formulation of kinematics and reference frames. When I studied kinematics, the idea of what is meant by a 'frame of reference' was never quite fully ...
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1answer
307 views

Find the coordiantes of a rectangle using vectors

I have two coordinates which are vertices of a rectangle. They form the diagonal of the rectangle. Is it possible, using vectors, to calculate the other two coordinates? I have tried calculating ...
2
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0answers
83 views

Evaluation of oscillating gaussian integral

I've problems to evaluate the following integral $$\int_{\mathbb{R}^3} dx \, dy \, dz \, \frac{e^{-i \Gamma |\vec{r}-\vec{r_0}|}}{|\vec{r}-\vec{r_0}|} \frac{e^{i \Upsilon |\vec{r}|}}{|\vec{r}|} ...
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2answers
42 views

Given a bunch of rectangles, find an enclosing rectangle.

Given below are a bunch of rectangles whose dimensions are listed in (x, y, w, h) format. Where, x, y are coordinates of left top corner of the rectangle while w ...
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1answer
96 views

Need a hint on what's wrong - polar coordinates

I'm asked to solve the following $$ \int^2_0 \int^\sqrt{4-y²}_0 \sqrt{4-x^2-y^2} dxdy $$ I thought about using polar coordinates: (1) $0 \le x \le \sqrt{4-y^2}$ is the upper half of a circumference ...
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2answers
418 views

How to verify a conversion to spherical coordinates?

Is it possible to verify if a conversion of an integral in Cartesian coordinates to spherical coordinates was done correctly other than revising it looking for mistakes? I mean, is there some kind of ...
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0answers
161 views

Change of coordinates in 3D

It's been a while since my last geometry class and I need some help in solving a very simple problem I have. I need to implement a zoom function in 3D in a piece of software I am writing. My system ...
2
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1answer
208 views

Proper change of coordinates

It's a really easy one for you guys. I'm performing a simple cylindrical change of variable from Cartesian coordinates, but I want to write it out properly and I'm stuck with the differential ...
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0answers
50 views

graph of moving object

let us consider following three picture grouped as in one picture suppose that we have following problem: during the $1$ hour,biker was moving around station $A$ and during this $1$,he did not ...
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0answers
45 views

Solving a system of equations

I'm trying to prove the existence of a solution to the system of equations $$c_i = \gamma x_i + (1-\gamma) \frac{x_i^2}{\sum_{j=1}^\infty x_j}$$ for $i\in\{1,2,....\}$ where $\sum c_i=1$. I am also ...
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2answers
20 views

How can I get the $(x,y)$ of a sub-line, which has 0.45 length of the original line, between two points?

Given two points $(x_1, y_1)$ and $(x_2, y_2)$, they forms a straight line. The target is to find a point $(x_t,y_t)$ between these two points, and the length from $(x_1, y_1)$ to $(x_t,y_t)$ is 0.45 ...
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0answers
30 views

How to figure out if a point is inside the bounds of a rotated rectangle [duplicate]

I'm trying to figure out an approach (or a formula) to determine if a point (x,y) is inside the bounds of a rotated rectangle. For this test we can assume that the rectangle is centered on the ...
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1answer
330 views

Transform between cartesian coordinate system and abstract coordinate system

I am trying to find a transformation that takes me between Cartesian coordinates and a pseudo-coordinate-system I have developed which is described as follows: Please first see the diagram below. ...
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1answer
174 views

Find meeting coordinates of two points

First of all, sorry for my English, because I am from Russia. The task is: We are given two points (see image) - $(x_1, y_1)$ and $(x_2, y_2)$. Point $(x_2, y_2)$ is moving and has a speed of ...
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3answers
2k views

project a point in 3D on a given plane

A point in a 3D space is given as $ P(x,y,z) $. I want to find the position of this point projected parallel to the normal on a plane Q defined by $3$ non-collinear points $ Q1(x1,y1,z1), ...
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1answer
84 views

find parameter for maximize area

suppose that we have Cartesian coordinate system.and suppose that we have three point which depend on parameter $t$,where t belongs to $(0,1)$;points are $A(cos(3-t),sin(3-t))$ $B(cos(t),sin(t))$ ...
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1answer
313 views

Homothetic transformation

Suppose that, we have a homothetic transformation in a rectangular coordinate system, with center origin $(0,0)$ and $k$. This homothetic sends point $A(2,3)$ to point $B(2x-1,x)$. My aim is to find ...
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4answers
75 views

A vector should more be thought an identity of an entity in space rathar than magnitude + direction?

Can I say that vector is more like a "unique identity" of an entity in space rather than calling it an entity with magnitude and direction ? For example a line. A vector $(10,10,0)$ is the identity ...
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3answers
274 views

How to check if three coordinates form a line

Assume I have three coordinates from a world map in Longitude + Latitude. Is there a way to determine these three coordinates form a straight line? What if I was using a system with bounds that ...
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2answers
271 views

Expansion of velocity in polar coordinates using kinetic equations

Why does total energy $$E=\dfrac{1}{2}\mu\mathbf{v}^2+U(r)$$ expand to $$E=\dfrac{1}{2}\mu(\dot{r}^{2}+r^2\dot{\phi}^2)+U(r)?$$ It's some form of the kinetic equations in polar coordinates. I know ...
4
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0answers
239 views

Orthogonal Coordinate Systems Intuition

I'd really love it if you could give some intuition on how to derive the $x$, $y$ & $z$ coordinates from all/any of the orthogonal coordinate systems in this list, how you think about, say, ...
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1answer
232 views

Convert spherical coordinates to Cartesian coordinates for a vector

So let's say I have a normalized vector $N$ given in cartesian coordinates and I have another normalized vector $V$, defined in spherical coordinates relative to the vector $N$. So $\theta_V$ is the ...
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1answer
38 views

Conversion of $F(x) = {1 \choose 0} (2t^2 - 3t + 1) + {3 \choose 1} (4t - 4t^2) + {1 \choose 2} (2t^2 - t)$

I have a textbook with a calculation step that is pretty unclear to me: $$F(x) = {1 \choose 0} (2t^2 - 3t + 1) + {3 \choose 1} (4t - 4t^2) + {1 \choose 2} (2t^2 - t)$$ $$= {-8 \choose 0} t^2 + ...