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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9
votes
1answer
3k views

Rotating a point in spherical coordinates around Cartesian axis

If I have a point in spherical coordinates, and I rotate it around one of the Cartesian axes, what will be the new spherical coordinates for the point? Both spherical and Cartesian coordinate systems ...
0
votes
2answers
188 views

What is the y-cooridinate for the point on the curve with x-cooridante 20?

What is the y-coordinate for the point on the curve with x-coordinate 20? $F. 160$ $G. 162$ $H. 164$ $J. 166$ $K. 168$ The explanation says "The correct answer is G. If the x-coordinate is 20, ...
0
votes
2answers
57 views

Spherical coordinate versor problem

I have to calculate $$ i_\rho \times i_\phi $$ it should be $$ i_\theta $$ but in my notes I have $$ - i _\theta $$ Which one is correct? How can I do this kind of operations without mistakes?
1
vote
2answers
3k views

Finding the points where a circle intersects an axis

A circle has the equation: x²+y²+4x-2y-11 = 0 What would be the coordinates of the points where the circle intersects with the y-axis and how would you calculate it?
4
votes
1answer
185 views

Changing local coordinates on a manifold by a diffeomorphism

This is the set up of my problem: Let $M$ be a manifold with local coordinates $x^1,\dots, x^n$. Let $x^1,\dots,x^n,\xi_1,\dots,\xi_n$ denote the induced coordinates on $T^\ast M$. Let $f:M\to M$ be ...
1
vote
0answers
112 views

Cartesian to geodetic conversion of 3D bounding box - How to calculate latitude and longitude from an axis aligned bounding box

I have a geometry with its vertices in cartesian coordinates. These cartesian coordinates are the ECEF(Earth centred earth fixed) coordinates. This geometry is actually present on an ellipsoidal model ...
8
votes
3answers
3k views

Direct formula for area of a triangle formed by three lines, given their equations in the cartesian plane.

I read this formula in some book but it didn't provide a proof so I thought someone on this website could figure it out. What it says is: If we consider 3 non-concurrent, non parallel lines ...
0
votes
1answer
97 views

Latitude and longitude to screen coordinates using “mapping points”?

I wrote a simple application which has a static image. I have 2 types coordinates for a point (or points if it is necessary): latitude and longitude; x and y for a screen. So I can get some ...
2
votes
0answers
109 views

Transition Functions for Cartesian Coordinate Systems

This is my first time using Mathematics SE (I've only used Physics and Astronomy before), so I apologize if this question is awkwardly phrased or incorrectly presented. I welcome any and all edits and ...
2
votes
3answers
103 views

Manifolds, charts and coordinates

Let's consider the manifold $S^1$ It is well known that we need two charts to cover this manifold. Nonetheless, we can cover the full space using a single coordinate $\theta$ which is just the angle ...
0
votes
1answer
49 views

Counting points in/on cuboid

Given a cuboid that extend in x,y,z axis such that |x|≤N, |y|≤N, |z|≤N where N is given and can have value up to 10^9.Now a shooter is standing at origin (0,0,0).He need to shoot on any of the ...
2
votes
1answer
44 views

Changing the length scale of the system of coordinates

Change the length scale on the axes of original system of coordinates, in which the equation $$y=x^3-px\qquad\text{(1)}$$ is plotted, i.e. introduce new coordinates $x_1$ and $y_1$ instead of ...
3
votes
2answers
77 views

Can a straight line be drawn from origin to co-ordinate X,Y?

Given a co-ordinate P(X,Y), can a straight line be drawn from origin to P, if there is wall existing with end points A(X1,Y1) and B(X2,Y2)? My Approach: I first of all wrote the equations from origin ...
1
vote
1answer
107 views

Solid angle subtended in latitude-longitude maps

I need to scale a latitude-longitude map with the solid-angle each "pixel" subtend. How can I obtain the said solid angle starting from the $\phi$ and $\theta$ angles? Thank you very much
1
vote
1answer
131 views

How to find the angle between two vectors?

Here, I would like to describe my requirements .. Let's say we have two vectors named $\bf A$ and $\bf B$. Two vectors are in different magnitude and opposite directions and lay on different planes. ...
3
votes
1answer
99 views

True or False. Non parallel lines in 3-space.

Two non parallel lines in 3 space must intersect in at least one point. True or False? I say false because you can have two perpendicular lines on x and y, but on a different "level" of the z-axis. ...
1
vote
0answers
268 views

For which real numbers $c$ is there a straight line that intersects the curve $y = x^4 + 9x^3 + c x^2 + 9x + 4$ in four distinct points?

For which real numbers $c$ is there a straight line that intersects the curve $y = x^4 + 9x^3 + c x^2 + 9x + 4$ in four distinct points? I don't quite the understand the solution which is in ...
1
vote
0answers
1k views

Radians : negative and positive values

Recently I have been reading books on DSP where I came across Polar co-ordinates. I understand that on Polar graph (4 quadrants) we have $0, \frac{\pi}{2}, \pi, \frac{3}{2\pi}$ and $2 \pi$ radians as ...
1
vote
1answer
208 views

Get position of a point with known distance between other points

If there are $(n+1)$ points in $m$ dimensional space, and we have known the Euclidean distances from one point "$B$" to the other $n$ points "$A_1,\ldots,A_n$", and known the positions of these $n$ ...
1
vote
1answer
99 views

How to find the surface element for the cylinder $x^2 + y^2 = r^2$?

So if given a surface (cylindrical) which has radius r and equation $x^2 + y^2 = r^2$, I want to work out the line element for it. How do I get it? I know the final answer has to be $dS^2 = r^2dϕ^2 ...
0
votes
1answer
290 views

How can I refer a 3D pose (position + orientation) to a different coordinate system?

I'm working on a robotics project where all poses and marker positions/orientations are stored as a matrix: $$ \mathbf{P} =\begin{bmatrix} \mathbf{R} & \mathbf{t}\\ ...
3
votes
3answers
1k views

Find X location using 3 known (X,Y) location using trilateration

I post this question in stackoverflow here and was advised it was best suited for here. I am trying to understand the maths behind trilateration, we have 3 access points (AP 1,2,3) and we know the ...
0
votes
0answers
30 views

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 ...
0
votes
0answers
42 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 ...
0
votes
3answers
4k views

Dividing line segments with ratios vs. fractions [closed]

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 ...
2
votes
1answer
106 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?
0
votes
1answer
133 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 ...
0
votes
1answer
323 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 ...
1
vote
2answers
356 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. ...
0
votes
1answer
36 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 ...
0
votes
1answer
6k 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 ...
0
votes
3answers
121 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 ...
0
votes
1answer
550 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 ...
0
votes
2answers
58 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 ...
1
vote
1answer
115 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 \; ...
0
votes
1answer
96 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: $[x,y,z] = A*s^2 + B*t^2 + C*u^2 + D*2st + E*2tu + F*2su$ ...
4
votes
1answer
55 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 $\sin\alpha x +\sin\beta y +\sin\gamma =0$ ...
4
votes
2answers
73 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) $3$ ...
1
vote
2answers
35 views

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 ...
0
votes
1answer
77 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 ...
3
votes
1answer
559 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 ...
4
votes
0answers
608 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: $$ x=r \cos(t) \\ y=r \sin(t) $$ ...
1
vote
1answer
49 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 ...
0
votes
2answers
129 views

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 ...
0
votes
1answer
47 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 ...
1
vote
0answers
34 views

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 ...
1
vote
0answers
39 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 ...
0
votes
3answers
53 views

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 ...
0
votes
2answers
52 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 ...
1
vote
2answers
50 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 = ...