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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3
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2answers
59 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
0answers
23 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
40 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. ...
2
votes
1answer
46 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
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0answers
97 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
56 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,pi/2,pi,3/2pi and 2pi radians as we move from one quadrant to ...
1
vote
1answer
64 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
38 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
32 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}\\ ...
2
votes
2answers
115 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
18 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
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0answers
28 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
0answers
28 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 ...
0
votes
3answers
432 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 ...
1
vote
1answer
31 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
28 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
56 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
46 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
20 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
418 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
40 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
207 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
43 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
40 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
42 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
39 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 $\sin\alpha x +\sin\beta y +\sin\gamma =0$ ...
2
votes
2answers
37 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
19 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
41 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 ...
2
votes
1answer
115 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 ...
3
votes
0answers
57 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
23 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
41 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
42 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
30 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 ...
0
votes
0answers
22 views

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. ...
1
vote
0answers
31 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
50 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
44 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
39 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 = ...
0
votes
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 ...
1
vote
2answers
43 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 ...
0
votes
1answer
37 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 ...
1
vote
0answers
15 views

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 ...
0
votes
1answer
38 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 $$ ...
0
votes
0answers
43 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. ...
0
votes
1answer
28 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 ...
1
vote
1answer
53 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 ...
0
votes
1answer
24 views

How does the transformation $u=x+y$, $v=x/y$ transform the first quadrant?

How is the region $(x,y) \in [0,\infty] \times [0,\infty]$ transformed under the change of coordinates given by $$u=x+y$$ $$v=x/y$$ Would appreciate any hints on how to find the image of such ...
0
votes
1answer
55 views

What are the coordinates of a point on a rigid body after a rotation in 3D Euclidean space, given the initial coordinates and a center of rotation

Main question Let ($x_p$, $y_p$, $z_p$) be the initial coordinates of a point $P$ on a rigid body in a right-handed 3D Euclidean space. Let ($x_r$, $y_r$, $z_r$) be the coordinates of a center of ...