0
votes
1answer
13 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 ...
0
votes
0answers
17 views

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 ...
1
vote
1answer
87 views

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 ...
0
votes
1answer
45 views

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.
1
vote
2answers
708 views

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 ...
3
votes
1answer
68 views

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 ...
0
votes
3answers
2k views

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. ...
0
votes
0answers
188 views

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 ...
0
votes
1answer
333 views

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 ...
2
votes
1answer
152 views

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 ...
2
votes
1answer
236 views

A question related to Plane and Sphere

The problem: A variable plane passes through a fixed point (a,b,c) and cuts the coordinate axes at P, Q, R (where none of P, Q, R is the origin). The co-ordinates (x,y,z) of the center of the sphere ...