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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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 $(x_0, y_0, z_0)$?
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1answer
24 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 ...
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22 views

Algorithm for vector space transformation [on hold]

In my text book I've got an example which is as follows: Create an algorithm which calculates coordinates of a point after a space transformation took place. Transformations may be scaling or ...
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1answer
25 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 ...
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1answer
19 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: ...
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31 views

Intesection point of feet of altitudes

If triangle has vertexes at $(x_1,y_1),(x_2,y_2),(x_3,y_3)$, is the intersection points of feet of altitudes $$x_h = \frac{x_1x_2(y_2-y_1) + x_2x_3(y_3-y_2) + x_3x_1(y_1-y_3) + y_1^2(y_3-y_2) + ...
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1answer
23 views

Solving for $x$ in terms of $y$ using coordinates

A line passes through $(4,1),(1,y),$ and $(x,2)$. What is the value of $x$ in terms of $y$? What equation do I have to use for this problem? $m=\frac{y_2-y_1}{x_2-x_1}$ , $y=mx+b$ , $y-b=m(x-a)$ I ...
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3 views

Underlying connections between parametric surfaces and co-ordinate transforms

I've recently been learning about parametric surfaces and surface integrals involving various co-ordinates systems. I was wondering, is there a fundamental connection between parametrization and ...
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2answers
91 views

Number of solutions of a simple equation

Problem How to count the number of distinct integer solutions $(x_1,x_2,\dots,x_n)$ of the equations like : $$|x_1| + |x_2| + \cdots + |x_n| = d $$ the count gives the number of coordinate points ...
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1answer
18 views

Trying to figure out coordinates of isoscleles triangle

I'm programming some application, which heavily depends of geometry. Let's say, in 2D coordinates system I have i.e. : Bxy = (5,-2) Cxy = (2,-5) ABlength = 5.5 ...
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1answer
25 views

How to find circumference origin position?

I need to find origin of circumference which is defined by two points and vertex angle of isosceles triangle: I've got radius of triangle by ...
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1answer
22 views

Equation Of A Straight Line Passing Through A Point and Having an Intercept

The question is as follows: "Find the equation of the straight line passing through (-2,-7) and having intercept of length 3 units between straight lines 4x + 3y = 12 and 4x + 3y = 3." I really ...
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3answers
24 views

Coordinate Geometry of triangle question

Can someone please explain how I can get coordinates for B using the slopes that are shown in the question? I'm not sure how I came to my solution where I tried to use y=mx+b. For e.g. to solve for ...
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2answers
21 views

Orthonormal basis in a cylindrical coordinate system

So I am supposed to show if these vectors make an orthonormal basis in a cylindrical coordinate system. $\vec e_p=\bigl(\begin{smallmatrix} cos(\theta )\\ sin(\theta )\\0 \end{smallmatrix}\bigr); ...
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0answers
13 views

Minimum and maximum points

The question is : Find the shortest distance from the point (2,1,-1) to the plane : x+y-z=1 . So can we solve this problem by using the rules of stationary points ( minimum points ) , if not , How ...
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1answer
27 views

defining a closed curve in cartesian coordinates

I am trying to implement a track in cartesian coordinates, such that X and Y coordinates are accepted and those are linearly interpolated. The problem is, I want to include circular shapes on ...
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1answer
18 views

How do I get the start and endpoint of a line using the middle point and the angle?

I have a line that goes from P1 to P2 in a 2D space. I have the location of the middle point of that line, and the angle of inclination of the line. The thing is that I don't know the length of the ...
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68 views

Elastic wave equation in curvilinear coordinates: how do you perform a coordinate change?

The essence of this question is that I don't know how to convert an equation from Cartesian coordinates into curvilinear coordinates, and would like to know how, preferably using the language of ...
5
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1answer
86 views

Transforming a PDE given basis vectors

I have a non-orthogonal coordinate system defined by $\mathbf x=\mathbf x(r,\beta,z)$, and so I can find the basis vectors as $$ \mathbf g_r=\frac{\partial \mathbf x}{\partial r},\quad\mathbf ...
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1answer
19 views

Calculate Coordinates

I have the following two circles (n1, n2). I know the coordinates of them. They are connected with a line. I also know the angle "alpha" and the diameter of the circles. Now I try to calculate the ...
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3answers
83 views

Volume of the solid bounded by the sphere $x^2 + y^2 + z^2 = 9$ and paraboloid $8z = x^2 + y^2$

Find the volume of the solid bounded above by the sphere $x^2 + y^2 + z^2 = 9$ and below by the paraboloid $8z = x^2 + y^2$ I'm having some trouble finding the correct limits of integration in ...
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2answers
70 views

Finding closest point perpendicular to B

Given: A = 8,4 B = 4,8 C = 4,4 D = ?,? From point C (4,4) (red dot) how would I find the coordinate that would be perpendicular to AB and CD being parallel to ...
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1answer
38 views

Having 2 coordinates putting the third coordinate on the closest 90 degree point

I've got a follow-up question for the previously asked and answered question here What I am trying to do now is that when I have a third coordinate I want it to be converted to the closest point on ...
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1answer
33 views

Having 2 coordinates calculating the 90 degree angle formula of the next point

I have 2 coordinates, what would be the 90 degree formula to the next point I am drawing? Say ...
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1answer
22 views

Calculating rectangle having 2 coordinates and 1 length

How could I calculate the other 2 points if I have a rectangle with 2 points and 1 length given? ...
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21 views

How to calculate end point of vector using quaternion?

How can the end-points of the three orthonormal vectors representing local coordinate system of point (p.x, p.y, p.z) be calculated given rotation represented by quaternion in global coordinate system ...
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48 views

What did homogeneous coordinates allow 19th century mathematicians to do?

I read about Mobius developing Barycentric and homogeneous coordinates, and I read about homogeneous coordinates and what they are and I'm totally on board with taking a line from the origin and ...
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59 views

Maximum product of lengths involving secant drawn to a parabola.

A chord is drawn from a point $P(1,t)$ to the parabola $y^2=4x$, which cuts the parabola at $A$ and $B$. If $PA\cdot PB=3|t|$, what is the maximum possible value of $|t|$? All I can infer is that the ...
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45 views

Computing area of triangle via equations of medians

For a triangle $ABC$, $B=90^\circ , AC=6$, equations of medians through $A$ is $y=2x+4$ and through $C$ is $y=x+3$. What is the area of triangle $ABC$? I'm really bad at geometry, and to make matters ...
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12 views

How do I convert between the different co-ord systems for Ray Tracing?

I am having trouble understanding how to convert (and what to convert) for my ray tracing program. At the moment I only have 3D to 2D projection transformation which is used to project the 3D world ...
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1answer
20 views

Coordinates change

Lets say our vehicle is moving at $50\frac{km}{h}$ ($31 mph$) for $15$ seconds only on $X$ or $Y$-axis (also on both). How much does the Geographic coordinates change in that time? I googled and ...
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1answer
33 views

Triple Integrals: Conversion

I'm currently in second year calculus and have come across a problem that I'm struggling badly to try and understand. The question is as follows: Sketch the region of integration of the following ...
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How do I determine for given two rectangles A & B, with B having constant dimensions, that B is more than 50% inside A? [duplicate]

I have 2 rectangles in a 2D plane, only in the first quadrant with limit 2000 x 2000: A (black) & B (red) Look at the attached image Both can change positions (coordinates, X & Y). B has ...
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1answer
112 views

Vector Algebra Coordinate Transformation

Let us look at two coordinate systems $K$ and $K'$ with axes, respectively, $(x_1,x_2,x_3)$ and $(x_1',x_2',x_3')$ and unit vectors ($\vec{e_1},\vec{e_2},\vec{e_3}$) and ...
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9 views

calculating position of a point knowing two reference lengths

Hi, I would like to know if there is a way to calculate a unique position for Point A knowing the lengths l1 and l2 which are variable string lengths. Point A can move within the range shown below. ...
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1answer
49 views

Locus of a point $P$ inside $\triangle ABC$

$P$ is a point inside $\triangle ABC$. $X$, $Y$ and $Z$ are feet of perpendiculars from $P$ on $BC$, $CA$ and $AB$ respectively. Find the locus of $P$ if $XY=XZ$ and $A \equiv (4,3)$, $B \equiv ...
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1answer
34 views

How to evenly space a number of points in a rectangle?

Say I have a rectangle, with variable width and height, for example lets use: width = 20 height = 30 I would like to put n ...
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1answer
32 views

How to represent two coordinate system transformations as one

I'm working on a system of relative euclidean coordinate systems. I'd like to define every coordinate system relative to a global coordinate system, which I'll refer to as [0]. Then, for example, ...
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1answer
14 views

Phase of relative coordinate in the complex plane

If we have two points $z_1=x_1+iy_1$ and $z_2=x_2+iy_2$ in the complex plane and define the relative coordinate $z=z_2-z_1$, we have that the length of $z$ is the Euclidian distance between the ...
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1answer
33 views

Voltage Distribution Inside a Cylinder [closed]

I was assigned this problem, and quite honestly I do not know where to begin. If I could get some help and an explanation of the Bessel function, also? Thank you. I know my conditions are: ...
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triple integral reduction

I have a triple integral of this kind $$\int_0^t{dx f(x)\int_{t-x}^{\infty}{dy g(y)\int_{t-x-y}^{t+\Delta t-x-y}{dz\delta(z)h(x,y,z)}}}$$ where $\delta$ is the Dirac Delta function and the other ...
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2answers
33 views

Calculating the lengh of $AG$ in a square

$ABCD$ is a rectangle and the lines ending at $E$, $F$ and $G$ are all parallel to $AB$ as shown. If $AD = 12$, then calculate the length of $AG$. Ok, I started by setting up a system of axes where ...
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1answer
13 views

Dealing with negative areas— coordinate geometry

Question: Find the area of a quadrilateral in the Cartesian plane, whose vertices are (-4, 5), (0, 7), (5, -5) and (-4, -2) My solution: [I meant to draw ...
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1answer
17 views

determine transform matrix given two points

You'll have to excuse me if this is a dumb question, but I am only familiar with the basics of linear algebra. I have the coordinates of the SAME point in two different coordinate systems. Is it ...
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9 views

Confusion about coordinate transforms

Lets say I have a camera aligned with the world coordinates system. I rotate it by 180 degrees around the z axis and then by 20 degrees around its new y axis. I have been reading about Euler angles ...
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1answer
18 views

Inverse rotation euler angles

I have three angles representing a rotation (Pitch, roll and yaw). I need the inverse rotation (working on coordinate system transforms). What I do now is transforming these angle to a rotation matrix ...
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2answers
102 views

Find the locus of points M the difference of the squares of whose distances from two given points A and B is equal to a given value c.

Find the locus of points M the difference of the squares of whose distances from two given points A and B is equal to a given value c. For what values of c does the problem have a solution? I am ...
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0answers
11 views

Pairing Two Point Clouds

So I have two point clouds $X$ and $Y$ each with $N$ points in the familiar $\mathbb{R}^3$ euclidian 3D space. I then have an inter-point distance $d(\vec x_i,\vec y_j)$ which is zero if $\vec x_i$ is ...
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2answers
14 views

Coordinate/matrix multiplication

If I multiply a 3d coordinate (padded with a 1 to make it a 4x1 matrix) with a transformation matrix, I get a 1x4 matrix which contains my new (transformed) 3d coordinate. Knowing that matrices must ...
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3answers
68 views

Trying to understand polar coordinate vectors

I'm trying to understand what the unit polar coordinate vectors (I'll denote them $\hat r$ and $\hat \phi$) are and if they form a basis for $\Bbb R^2$. So from what I understand, $\hat r$ points ...