# Tagged Questions

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### 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 ...
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### Mapping between two unknown 3D coordinate systems from common motion

Coordinate systems A and B are rigidly linked in an unknown way. The platform then moves and the motion vectors [RA|TA] and [RB|TB] are calculated in each coordinate system. They are parallel but not ...
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### The Puzzle of Locating Points in a Quadrilaterally-Faced Hexahedral Creature

The Disclaimer This is NOT homework... I designed the story. I thought a name MIT would be funny, while something along the line of TULSA or SU will still be decent. I know the algorithm to Q3 and 3D ...
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### Geometry finding area problem

A regular 2N -sided polygon of perimeter L has its vertices lying on a circle. Find the radius of the circle and the area of the polygon.
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### Finding the locus of the midpoint of chord that subtends a right angle at $(\alpha,\beta)$

There is a circle $x^2+y^2=a^2$. On any line that cuts the circle in two distinct points(it is a secant), the points of intersection with circle are taken and at those two points I draw the tangents ...
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### maximising the angle $\theta$

OK, suppose I have two points in cartesian coordinate system, say $P(x_1,y_1)$ and $Q(x_2,y_2)$. I have a line as well, that is, for simplicity $$y=mx$$ Assuming that $$y_1\neq mx_1,y_2\neq mx_2$$ I ...
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### Proof of test of collinearity and coplanarity

Statement : If there are 3 points with position vectors a, b and c. Then the points are collinear if and only if there exist scalars x,y,z, not all zero,such that x a + y b +z c = 0 where x+y+z =0. ...
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### Calculate coordinates of the a point in space with hypotenuse and two angles given

I have a cylinder with a length of $2$, and two angles for rotation around two of the axes. Functions for that are named $\text{RotX}$ (rotation around X axis) and $\text{RotZ}$ (rotation around Z ...
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### transforming vector potential with a coordinate rotation

In electrodynamics, given the vector potential $\vec{A}$, the magnetic field is defined as: $\vec{B} = \nabla \times \vec{A}$ I'm having trouble figuring out how a coordinate transformation (a ...
### How to find the $P_2$ when $T_1P_1=T_2P_2$
$T_1$ and $T_2$ are $3 \times 3$ homogenous transform matrices. $P_1$ is the $3 \times 1$ matrix with $x, y$ coordinates of point $P_1$. What I am trying to do here is trying to get $x, y$ coordinate ...