Coordinates of a point in 3D provided connecting points are known

AI Thread Summary
To determine the coordinates of point C given points A, B, and the distance from B to C along with angle ABC, the discussion highlights that the problem lacks sufficient information for a unique solution. It is noted that in three-dimensional space, multiple points can satisfy the conditions, resulting in a circle of possible locations for C. Additionally, the introduction of points C and D, along with their respective angles and distances, complicates the problem further, as finding two unknown points with only one length and three angles is also impossible. The participants suggest that a simpler method may exist but emphasize the need for more data to achieve a definitive answer. Ultimately, the discussion underscores the complexities of solving for coordinates in 3D space with limited information.
joinforfun89
Messages
4
Reaction score
0
Hi ,Given 3 points A[x1,y1,z1], B[x2,y2,z2] and C, and given the distance between B and C is known and the angle ABC is supplied. How do we ascertain the coordinates of the point C ?

I can calculate the dot product using the angle, by defining vectors BC and AC and then use the distance formula to get another equation for the coordinates of C. But I have a hunch that there is a simpler way to do this. I need to program this, and therefore the requirement for a simpler solution.

If there is a derivation that you know please point me towards it.

Thanks a lot in advance.MORE Information Added:

I didn't include all the information earlier and yes Mathman is right that as stated this problem doesn't have a unique solution. This is actually a smaller part of the bigger problem I have. Here it goes.

A-B-C-D are 4 points. We define rx = length(B-C), angle, eta = (A-B-C) and angle theta = (B-C-D) and the torsion angle omega= (A-B-C-D). What I really need to do is to find the coordinates of C and D provided that I have the new values of rx, eta, theta and omega. Any pointers would be welcome.

Thanks again.
 
Last edited:
Mathematics news on Phys.org
The problem as stated does not have enough information to get a unique solution for C. Since the problem is 3d, there will be a circle of points satisfying the requirements.
 
mathman said:
The problem as stated does not have enough information to get a unique solution for C. Since the problem is 3d, there will be a circle of points satisfying the requirements.

I have added more information; please take a look if you get a chance ! Thank a lot.
 
You want to find 2 unknown points knowing 1 length and 3 angles. That can't be done either.
 

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »
Thread 'Imaginary Pythagorus'

Thread 'Imaginary Pythagorus'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
View full post »

Similar threads

B Reprise: Calculate the distance between two points without using a coordinate system
Replies
1
Views
2K
I Polygon Coordinates given the Area and Center point
Replies
10
Views
2K
I Given a triangle ABC, on which side of the triangle does the point D lie?
Replies
6
Views
2K
I Finding the coordinates of a point on a sphere
Replies
7
Views
3K
I Closest point on a plane to a point near the plane
Replies
6
Views
3K
I Equation for circle points in 3D
Replies
3
Views
3K
I Five points in space with rational distances that are not co-linear
Replies
13
Views
2K
I Finding vertex of a 3D Triangle on a Plane
Replies
3
Views
2K
MHB Finding exact 3d coordinates in a falling pipe system with corners
Replies
20
Views
4K
I Help creating a coordinate system for a robotic arm
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top