# Tagged Questions

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### Calculating the divergence of a central vector field.

I am trying to calculate the divergence of a central electric field, namely the electric field due to a point charge and my book begins like this: http://imgur.com/bW9tPEZ However in the last line I ...
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### Definite integral-dot product

I have an integral equation containing dot product $$\int_{0}^{L} \left(\frac{a}{L}.b(s)\right)\mathrm ds\tag 1$$ Data Given a is a constant vector of size 3 b(s) is a varying vector of size 3 " . ...
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### Metric for vector sets

I am currently working on a classification algorithm. Each class is represented by a set of 3D vectors. The cardinality differs for each class. The order of the vectors in a set is completly random. ...
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### Gradient is covariant or contravariant?

I read somewhere people write gradient in covariant form because of their proposes. I think gradient expanded in covariant basis i , j , k so by invariance nature of vectors, component of gradient ...
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### How can vectors with different units (position, speed, …) “share” the same space?

My question is too stupid to be googled, so I'll ask it here (because I didn't get any answers from google). Context: I have a three dimensional space and the units for $x,y,z$ are given in meters. ...
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### vector question assistance

let there be 2 lines: $(2,-3,1) + s(3,-2,1)$ and $(2,-1,-3) +t(3,-2,1)$ which are parallel to each other. find the formula of the plane determined by them. my try: a vector perpendicular to ...
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### algebraic representation of a line in 3d

Is an algebraic representation of a line in 3d possible, or there can be only a parametric one?
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### Vector calculation question

the points a b c d are concordantly ( 1,2,-3) , (-1,2,1) , ( 0,1,-2) , ( 2,-1,1) find formula of the plane going thorugh d and which is pararlel to plane abc calculate the volume of pyramid abcd. ...
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### Vector pyramid question

Suppose we have a pyramid with two vectors known, as well as the angle between them...if we mutpliy their size by each other mutiply by the sine of the said angle and then by sixth, will we get the ...
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### A question about vector fields and divergence

I am reading the paper http://www.goshen.edu/physix/mathphys/gco/TensorGuideAJP.pdf in order to gain a basic understanding about tensors. I had some difficulties about understanding some definitions. ...
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### Finding loci of possible points satisfying vector simultaneous equations

I recently had an exam and a question came up which I was only partially able to answer. The question was the following: Let $\vec{a}$, $\vec{b}$ and $\vec{c}$ be constant vectors in ...
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### Is there a function to tell if two probability vectors' max values are in the same dimension?

Is there a method or function to tell two probability vectors' max values are in the same dimension? Or Is there a bound for the angle of two normalized probability vector which their max values are ...
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### Find eigenvector of the linear operator

Task is to find an eigenvector of the following linear operator: $f \to \int^{x}_{-x} f(t)dt$ in the linear span $\langle cos(x), sin(x), ...,cos(mx),sin(mx)\rangle$. I know how to find eigenvectors ...
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### Find dimension of the intriguing vector space

We are given vector space of polynomials over $\mathbb R$ of two variables with powers not higher than 2013. Let's consider subspace $V$ which contains such polynomials $f$, so following holds for ...
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### Field of vector fields

For every point $A$ outside a sphere with radius $a$, there's a field $$F= \frac{K}{r^4d^2}$$ where $r$ is distance between point $A$ and the center of the sphere, and $d$ is distance between point ...
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### evaluating a flux integral

Question: "Region V, of unit volume, is bounded by the closed surface S. Given the vector field $\mathbf{F}=\langle 7x,2y,5z\rangle$, evaluate: $$\int_S \mathbf{F}\cdot\mathbf{dS}$$ I guessed that ...
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### How are vectors defined in terms of sequences?

I'm reading this Wikipedia article on sequences Sequence where it mentions 'Sequences over a field may also be viewed as vectors in a vector space.' under vectors section. I'm not able to grasp this, ...