Intersection point between n-vector and n-sphere

[7toni7]

Hello,

I'm trying to compute the intersection point between a n-dimensional vector and a n-sphere.
Do you know how to perform this? is it the same than 2 and 3 dimensions?


I can't really find much information about this topic.
Thank you very much,

 

[lavinia]

Hello,

I'm trying to compute the intersection point between a n-dimensional vector and a n-sphere.
Do you know how to perform this? is it the same than 2 and 3 dimensions?


I can't really find much information about this topic.
Thank you very much,

what have you tried so far?

 

[meldraft]

The statement is quite ambiguous as in general a vector doesn't need to have a common point with a sphere. Even if it's centred at the sphere's origin, its magnitude might be less than the radius of the sphere. You need to attach your vector to some point for this question to have meaning! Maybe you mean the intersection between an n-sphere and the n-line whose direction is defined by an n-vector that originates from a certain point? If so, what is the centre of the sphere, and what is the vector origin point?

 

[7toni7]

Hello,

Sorry, I did not explain very good.

Suppose that we have one n-sphere. Inside it, we have a n-point (this point different of the origin, it is another point named H).

So, I have to compute the intersection of the line (that goes from the origin of the n-sphere passing from H) with the n-sphere. do you understand? is it possible?

Thank you in advance again,
Best.

 

[blue_raver22]

I appreciate your interest in this topic. The intersection point between a n-dimensional vector and a n-sphere can be computed using the same principles as in 2 and 3 dimensions, but the calculations may be more complex due to the higher dimensionality. In general, the intersection point can be found by solving the equation of the n-sphere and the equation of the vector simultaneously. Depending on the specific parameters of the n-sphere and vector, this may involve using techniques such as matrix algebra or multivariate calculus. I suggest consulting a textbook or seeking guidance from a mathematician or computer scientist for a more detailed explanation and step-by-step process. Best of luck with your research.