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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Find the intersection of three bisection lines

Let $p_1 = (a_1, b_1), p_2 = (a_2, b_2), p_3 = (a_3, b_3)$ be three, non-colinear points in the plane. For each pair of these points, let $L_{ij}$ denote the line segment from $p_i$ to $p_j$. (a) For ...
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49 views

How to find the equation of a line which intersects these lines at 90 degrees?

How to find the equation of a line which intersects these lines at 90 degrees? $p\equiv \dfrac{x}{2}=\dfrac{y+1}{0}=\dfrac{z-2}{1}$ $q\equiv \dfrac{x-1}{1}=\dfrac{y-2}{1}=\dfrac{z+5}{0}$ Since the ...
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1answer
12 views

Find a vector in cartesian coordinates given its relative location to another vector in spherical coordinates

Here is my problem: -I have an arbitrary normalized vector N in cartesian coordinates -I am trying to find normalized vector M, also in cartesian coordinates -I am given the azimuth and polar ...
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37 views

An error in Wikipedia? (trigonometry)

https://en.wikipedia.org/wiki/N-sphere In "Spherical coordinates" section the hyperspherical coordinates are results of arccosinus function. In some other sources there is arccotangent instead: ...
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1answer
234 views

Find parametric expression of an arc given its start point, end point and central angle in 3D cartesian coordinate system

In a 3D cartesian coordinate system, the coordinates of start point and end point have been given as $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$. If the central angle of the two points (the one smaller ...
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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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11 views

Parabolic Coordinates Radius

Given Cartesian $(x,y,z)$, Spherical $(r,\theta,\phi)$ and parabolic $(\varepsilon , \eta , \phi )$, where $$\varepsilon = r + z = r(1 + \cos(\theta)) \\\eta = r - z = r(1 - \cos( \theta ) ) \\ \phi ...
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18 views

Find coordinates for point on circle

We got two points on circle and we know about center angle between two points.If we know coordinates of center $(x_1,y_1)$ and point $A=(x_2, y_2)$ and angle $\alpha$, how can we find the coordinates ...
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17 views

Fit cartesian coordinate system to point cloud

I have a cloud of points that initially lie in a plane and have a coordinate system attached to them. I then displace the points slightly, and I want to find how a 'best fit' of the coordinate system ...
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1answer
20 views

Angle between planes , when only two points are given

Find the equation of plane passing through points $[1,0,0]$ and $[0,1,0]$, and making an angle of $45°$ degree with the plane $x + y - 3 = 0$.
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1answer
206 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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225 views

Minimum number of lines covering n points

Let there be n points in the plane. I want to know the minimum number of horizontal and vertical lines covering all the points in the plane. My initial approach started like this, 1) for each point I ...
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2answers
40 views

Tangent definition

As far as the definition of a tangent goes it is a line that touches a curve only at one point. Now let us consider the sine function .At (pi)/2 it attains its maximum value and so does it at ...
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1answer
39 views

Scalar products and partitions of Hypercubes

My questions relate to scalar products defined in $\mathbb{R}^{n}$ and partitions of hypercubes. Take $s \in \mathbb{R}$, $\xi, \eta \in \mathbb{R}^{n}$. My first question is why is it possible to ...
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1answer
22 views

rotation matrix to axis angle

from wikipedia the above rotation matrix has a rotation of -74 degrees. What does it mean "around the axis (−1⁄3,2⁄3,2⁄3)"? How can I determine how many degrees is rotated on X axis, Y axis and Z ...
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1answer
29 views

Convex Sets and extreme supports

Let the set $S$ in $R^n$ consists of the origin $0$ and $n$ lineary independent vectors $T_1, \ldots, T_n$. Show that $C(S)$, the convex hull of of $S$, is the intersection of its extreme supports, ...
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1answer
34 views

Geometric reasoning and triangular coordinates

The following is from a book: I do not understand the sentence "... the point $(t_1, t_2, t_3)$ can be plotted by plotting $(t_1 = t_3, t_2 = t_3)$...", what is meant by the point $(t_1 = t_3, t_2 = ...
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1answer
209 views

Find coordinates of n points uniformly distributed in a rectangle

I have a rectangle R of width W and height H. I have N points inside this rectangle. I need to find an algorithm to position my points in the rectangle in the most uniform way possible (no overlaps, ...
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1answer
45 views

“Rigorous” definition of Cartesian coordinates

I, like most, first learned about Cartesian coordinates very early on in my educational career, and so the most instructional way to think about them was that you place down some perpendicular lines ...
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1answer
163 views

Spherical coordinates of a unit vector around a normal $N$

So if I have a unit normal for a surface $N(x,y,z)$ and an incident unit vector $V(x,y,z)$ to that surface, how would I represent the vector V in spherical coordinates relative to the normal?
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1answer
13 views

Rotation of velocity vectors in Cartesian Coordinates

I want to rotate a $(X,Y,Z)$ coordinate-system around it $Z$-axis. For the coordinates this can be done with the rotation matrix: $$ R_Z(\theta)= \begin{pmatrix} cos \theta & -\sin(\theta) & ...
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1answer
16 views

How to draw a straight line and determine the gradient from the graph?

The following gives experimental values of two variables $x$ and $y$ which are known to be connected by a relation of the form $xy=a+bx$. So, this information was given in a table. $x=0.4,y=22.0$ ...
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How to move coordinate systems using rotation matrices.

I am having some trouble with this question. I understand that the rotation matrix will be 4x4 and that the first 3 columns will just be $u$, $v$ and $n$ transposed but I dont know what I am ...
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37 views

Using Cylindrical Coordinates to Compute Curl

I am given a vector field $\vec{A} = A_\rho \space \hat{e_\rho} + A_\phi \space \hat{e_\phi} + A_z \space \hat{e_z}$, and I am supposed to use the unit vectors (provided below) in cylindrical ...
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30 views

How to find the center of one side of a Quadrilateral

If I have a rectangle drawn in perspective and I know the coordinates of points A, B, C, D, how do I calculate the coordinates of point E? Which equates to the center of the bottom line if not drawn ...
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23 views

Find the coordinates of P.

A trapezium ABCD, AB parallel to DC, BC is perpendicular to both AB and DC. $A (4, 2), B (16, 8), C (13,14), D(5, 10)$. Lines AD and BC produced to meet at P. Find the coordinates of P. I tried to ...
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17 views

Inverse Rotation - Original X / Y values

Really stumped. I'm currently writing a program and I am given a rotated rectangular object on a 2d plane. The object has been rotated about it's center point and I need to find out how to get the ...
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1answer
112 views

What do we know about non linear coordinate systems?

I first learned about coordinate systems by Gelfand and I knew that we basically have two axis x and y with origin O and some unit vectors $\hat i$ and $\hat j$ and if $\vec{OA}=x\hat i+y\hat j$ then ...
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0answers
21 views

Finding coordinates of nodes in a graph

I have a complete graph in which the edges represent the euclidean distance between the nodes which is known. Assuming a node to be (0,0), I want to find (approximately) the coordinates of other ...
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29 views

A sufficient condition for a convex body to lie completely inside another convex body?

Suppose we have two convex bodies in 3D space. Let’s call them $B_1$ and $B_2$. Let’s denote their projection curves on the xy plane by: $P_{1xy}$ and $P_{2xy}$, on the yz plane by: $P_{1yz}$ and ...
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124 views

Jacobian of Fourier Transformation

I am trying to calculate the Jacobian determinate of the Fourier transform which I stumbled upon when studying the Path Integral in Quantum Field Theory. I know the answer should be $1$ but I don't ...
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1answer
17 views

How can I transform coordinate systems with quaternions?

I have a coordinate system 0 which I'd first like to rotate about its z-Axis which gives me system 1, and afterwards rotate system 1 about its y-axis which gives me system 2. See picture: Both ...
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Detect Regions Described By Lines in Rectangular Coordinates

Need some help from the superior math minds here. This problem is part of a software project. Essentially, I have a Cartesian grid. The user can create lines by plotting points (every 2 points ...
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1answer
26 views

Find the equation of the line.

Find the equation of the line passing through the point $(5,7)$ and parallel to the line $5x+4=0$ If I say $m=5$, how should I find $c$? There is no $y$ in the equation!
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Find the equation of the straight line.

Find the equation of the straight line that is parallel to $2y-x=7$ and bisects the line joining the points $(3,1)$ and $(1,-5)$. So, I found the gradient = $\frac{1}{2}$ And I solved the midpoint: ...
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1answer
298 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
41 views

Transfer Transformation from Physics to Vector Graphic

Upfront, I am not a professional in Maths and hope that the formulation of my question describes the problem well enough. I am creating a jump'n'run game, which uses a physics engine (Box2D) and SVG ...
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How to use geometry to express unit vectors of spherical coordinate system in terms of Cartesian unit vectors

It's quite easy to express unit vector $\hat{r}$ in sum linear combinations of Cartesian unit vectors $\hat{x}$, $\hat{y}$ and $\hat{z}$. But I am not sure how I can use geomtery to find a Cartesian ...
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How to find coordinates of a point on a 3D cylinder in Cartesian system if any one point on cylinder and dimensions of cylinder are known?

Consider a cylinder of known dimensions inserted in 3D cartesian space. I know the cartesian coordinate of one point located on the surface of cylinder. Using this information I want to find out the ...
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38 views

Find the coordinates of $P, Q, R$.

In triangle $PQR$, $A(-2,3), B(5,-1)$ and $C(-4,-7)$ are the midpoints of $PQ, QR$ and $PR$ respectively. Find the coordinates of P, Q and R. I really can't understand how to begin....Please hint :'( ...
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1answer
31 views

Mapping points on a plane in space onto a coordinate plane

Is there a way to isometrically map points on a plane in space onto a coordinate plane? So for example, given the three points $\left( 1,1,0 \right)\;, \left( -1,0,2 \right),\; \text{and }\left( ...
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3answers
216 views

What is wrong with this method for a rotated and shifted parabola?

$(x+2y)^2=4(x-y)$ Disecting the above parabola is the question. (vertex, axis,tangent at vertex,etc). So at first what I thought of was making its equations at LHS and RHS perpendicular. I thought ...
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1answer
470 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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41 views

Determining if a point is inside two planes

I have two planes(Plane 1 and Plane 2) the normals ($n_1$ and $n_2$) of which are known to me. How do I determine if a point is inside the two planes? By inside I mean the 3d space between Planes 1 ...
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Converting Euler Angle z-y'-x'' sequence to heading

I'm trying to convert a set of Euler Angles to a heading $(0-360)$ degrees. The Euler Angles use the $\ x-y'-x''$ sequence headings, using $\ \psi, \theta, \phi$ as the rotation angles, respectively. ...
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2answers
20 views

How to find the perpendicular distance from B to AC?

"Find the area of triangle $ABC$ with vertices $A(2, 1), B(12, 2) $and $C(12, 8)$. Hence or otherwise, find the perpendicular distance from $B$ to $AC$." I found the area, which is 30 units by find ...
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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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3answers
64 views

Why are the axes in coordinate geometry perperndicular?

In coordinate geometry, the $x$ and $y$ axis are perpendicular to each other. But is there any special reason for this (other than to make it simple)? Will coordinate geometry have contradictions if ...
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2answers
41 views

Show that the four points given below are the vertices of a rhombus.

Show that the four points, $(5, 8), (7, 5), (3, 5)$ and $(5, 2)$ are the vertices of a rhombus. I tried solving it, by finding out the distances by using the formula $\sqrt{(x_{2}-x_{1})^2 + ...
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A method of calculation coordinates in order to implement it to a code language!

lets say that we have three points A(xa,ya,za), B(xb,yb,zv), C(xc,yc,zc) with known coordinates in 3d space. Is there a method to calculate the coordinates (x,y,z) of another point D for which the ...