Questions on coordinate systems, a geometric method where a point in n-dimensions is assigned a corresponding n-tuple of numbers.

learn more… | top users | synonyms

1
vote
1answer
22 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) & ...
2
votes
1answer
43 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 ...
1
vote
1answer
60 views

Definition of smooth maps between manifolds

Here is a page from Guillemin-Pollack's differential topology: My question is: At the bottom he defines $df=d\psi\circ dh\circ d\phi^{-1}$. Why doesn't he just define $df=dh$, like here: ...
0
votes
1answer
30 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. $x=0.4,y=22.0$ ...
0
votes
0answers
25 views

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 ...
1
vote
1answer
52 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 ...
0
votes
0answers
24 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 ...
1
vote
0answers
29 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 ...
0
votes
0answers
33 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 ...
0
votes
0answers
19 views

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 ...
0
votes
1answer
34 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 ...
0
votes
1answer
27 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!
0
votes
2answers
34 views

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: ...
1
vote
1answer
59 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 ...
-1
votes
1answer
112 views

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 ...
-1
votes
1answer
47 views

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 ...
0
votes
3answers
42 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 :'( ...
1
vote
1answer
53 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( ...
0
votes
0answers
69 views

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. ...
0
votes
3answers
47 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 ...
0
votes
2answers
33 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 ...
1
vote
3answers
110 views

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.
1
vote
3answers
74 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 ...
0
votes
2answers
85 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 + ...
6
votes
1answer
126 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 ...
3
votes
3answers
248 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 ...
1
vote
0answers
16 views

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 ...
0
votes
0answers
8 views

Given U,V<->X,Y trnslation formula explanation

Well in a text book (about numerical analysis methods to do a polynomial interpolation in bivariate functions). The following piece of text/functions is just given, without much explanation. The goal ...
1
vote
3answers
48 views

How to find location of a point for a rectangle

I have a circle with a line that is drawn through it at two points. I have the coordinate for the center of the circle, the two coordinates where it intersects the circle and the radius as well. I ...
1
vote
1answer
47 views

Equation of a plane through intersection of two and parallel to other

I have got two planes $$x+y+z=1$$ and $$2x+3y-z+4=0$$ . I am required to find a plane by intersection of two and parallel to $x$ axis . I think the plane parallel to $x$ axis so Simply $P1+kP2=0$ ...
2
votes
1answer
98 views

Best way to plot a 4 dimensional meshgrid

I have $4$ variables $X$, $Y$, $Z$ and $C$, and I want to plot these on a graph. Usually I would just plot the surface $X$, $Y$, $Z$ and then use color to represent the $4$th dimension, as shown ...
0
votes
1answer
17 views

Proving the existence of a ____ number of conditions under a rotation of coordinates.

I'm reading a section on Rotation of Coordinate Systems and this is throwing me off: 'In n-dimensional space, the rotation matrix will have $n^2$ elements, upon which orthogonality relations place ...
2
votes
1answer
30 views

Coordinates of sector of circle

I know the coordinates of one point on a circle, this point is part of a sector. I know the angle of the sector at the centre of radius, I know the radius and I know the arc length. How do I calculate ...
0
votes
1answer
29 views

Get yaw to point at X and Y values (2D)

I have $X$ and $Y$ coordinates. I also have another object. I need to figure out how set the yaw of the second object to point at the $X$ and $Y$ coordinates. How can I go about doing this?
1
vote
2answers
86 views

Let PQR be a right angled isosceles triangle right angled at P (2,1). If equation of line QR is $2x+y=3$, equations of PQ&PR

Let PQR be a right angled isosceles triangle right angled at P (2,1). If equation of line QR is $2x+y=3$, find combined equation of pair of lines PQ and PR.
0
votes
2answers
79 views

solving 3-d coordinates from x, y and z distance

I working with WiFi positioning and i want to know the exact coordinate where I am. Here is the problem..
1
vote
1answer
31 views

How to get coordinates of some area

I have a rectangle and I divide it into 8 triangle with same size. Top left corner is origin. I want to check that if a point is inside the black area or not. Lets say point's x coordinate is pointX ...
3
votes
2answers
113 views

What is (fundamentally) a coordinate system ?

Consider the following construction of vectors and points. Let's start with a vector space, or more specifically a coordinate space $F^N$ over a field $F$ and of $N$ dimensions. The elements of this ...
0
votes
3answers
83 views

Origin in vector space?

In the wikipedia article about vector space I do not understand this sentence Roughly, affine spaces are vector spaces whose origin is not specified. A vector space does not need an origin. When ...
0
votes
0answers
29 views

symplectic coordinate change in tangent space

Given is the Hamiltonian system with energy function $$H(q,p) = \sum_{i = 1}^{2} \frac{p_{i}^{2}}{2m_{i}} + m_{i}V(q_{i}) = H_{0},$$ where $H_{0}$ is some positive constant and the potential energy ...
1
vote
1answer
139 views

Rigorous definition and relations between point/vector/affine space/vector space/basis/frame/coordinate system

I am trying to understand the exact relation between all these things: point vector affine space vector space basis frame coordinate system Can you explain me rigorously (in the mathematical ...
1
vote
1answer
57 views

Locus of center of circle.

Consider two circles with radii $a$ and $b$ and centers $(a, 0)$ and $(b, 0)$ respectively with $0 < a < b$. Let $c$ be the center of any circle in the crescent shaped region M between the two ...
0
votes
1answer
99 views

What are the coordinates of the ends of the latus rectum of the parabola $x^2 - 2y + 2 = 0$? [duplicate]

I've already graphed the parabola . i just don't know how to locate it's focus and the ends of it's latus rectum. On my graph, the vertex is on (0,1). Please help me with this. ASAP.
0
votes
1answer
22 views

Determining object rotation

I have an 8x8 square(room) with an object in it at the coords of (0, 0). If I rotate that square clockwise once, that object is now at (0, 7). I do it again an it's at (7, 7), and once more it's at ...
1
vote
1answer
82 views

Calculate possible intersection point of two lines

I'd like to know the $I$ coordinates $[x, y]$. $I$ is the possible intersection point of line $|AB|$ with $|XY|$ and $|X'Y'|$. Values that are known: Angle $AIX$ and $AIX'$ Coordinates of points ...
0
votes
1answer
13 views

Position Value in a Triangle

I have a triangle. Each of the 3 corners is assigned a different value. Lets say corner 1 is 100, corner 2 is 200, and corner 3 is 300. I want to pick a coordinate in the middle of the triangle and ...
1
vote
1answer
27 views

Possible path of a fixed length formula

I am looking for a formula that gives me all possible combinations of getting from point A(ax,ay) to point B(bx,by) using a ...
2
votes
1answer
66 views

How do I calculate a point's coordinates on a circle’s circumference

I have got a circle with radius $r$ and center point $c_x$ and $c_y$. Known values: - $c_x$ and $c_y$ - $r$ - length $AR_a$ - length $BR_b$ Angle between point $A$ and the radius $r$ is unknown ...
2
votes
1answer
31 views

A coordinate geometry question.

On pg. 46 of "Coordinate geometry" by S.L. Loney, the following question has been posed: Show that the equations to the straight lines passing through the point $(3,-2)$ and inclined at $60^\circ$ ...
0
votes
0answers
34 views

Looking for certain functions or a coordinate transform respectively

I want to generate an image of the mandelbrot set. That means to map the x-y-coordinate-system, where the mandelbrot set lives (e.g. x:-2 .. 1; y:-1.5 .. 1.5) to an screen coordinate-system u-v (say ...