# Questions tagged [vector-calculus]

Questions on dealing with vector calculus functions of Mathematica such as Grad, Div, Curl, Laplacian and their representations in various coordinate systems.

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### Efficiently finding spheres furthers apart along and perpendicular to a given direction

Setting I am dealing with a box of spheres, all having the same radius and inserted into a finite box size without any overlaps. Along a given direction $\mathbf v$, I am trying to find: (a) The two ...
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### Generating random vectors using Mathematica and an inequality

Consider $n$-dimensional vectors $c^i = \left(c^i_1, c^i_2 ...c^i_n \right)$ , whose entries are complex and generated at random. These vectors are normalized such that $$|c^i|^2 = 1.$$ Using ...
477 views

### Finding surface normal for 3D region at a specific point

I would like to find the surface normal for a point on a 3D filled shape in Mathematica. I know how to calculate the normal of a parametric surface using the cross product but this method will not ...
465 views

### Computing the intersection area of two disks in 3D

Closely related to this question about highlighting intersection of two disks, I am trying to figure out if one can do so similarly for disks embedded in $3D$ (e.g. in a bounding box). The difference ...
38 views

### Obtain the vector potential and magnetic vector of infinite wire carrying charge

I'm working on the question above, but I'm really stuck for days. my goal is to implement the following Problem in Mathematica. Any help would be appreciated. I want to evaluate the following ...
50 views

### Find vectors describing two interconnected pyramids in Euclidean space

I need the help of competent linear algebra specialists in Mathematica. In the Euclidean space, two tetrahedrons are turned at different angles. Their vertices coincide with the beginning of the base ...
59 views

### Summations on Variables with subscripts

One of my equations uses a set of variables which ultimately for a set of certain values gives a list of 8 numbers: c=13.9506 (31 - k) following cc(sub k) = Round[Table[13.950621339931203...
50 views

### Using Grad and NDSolve with vector variables

A simple orbital model might be developed like this: ...
140 views

### How can I use a unit vector notation found in physic texts?

In physics (I'm thinking of Taylor's Classical Mechanics or Griffith's Classical Electrodynamics) it is common to use "hat" vectors to denote unit vectors like $\hat{x}$ or $\hat{r}$. If I wanted to ...
244 views

### Line Integral Difficulty

I am having difficulty with the following question: Compute the line integral of $$f(x,y)=\frac{xy}{1+x+2y},$$ along the unit quarter-circle in the first quadrant from (1,0) to (0,1). My problem ...
55 views

### Error when trying to solve elastic PDEs using FEM: “Compile::argcompten: The comparison, LessEqual, is invalid for tensor arguments.”

I'm trying to solve the following linear elastic problem: The pairs of numbers beside each node is the coordinates in meters. The loads are in Newtons. The part of codes that probably have no ...
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### Verifying equality $(\vec a \times \vec b)^2 = \left| \vec a \times \vec b \right| ^2$

I'm trying to verify the equality $(\vec a \times \vec b)^2 = \left| \vec a \times \vec b \right| ^2$ in Mathematica. How can I do it? Thank you for your time.
I am trying to use mathematica to generate explicitely a tensor. I know multiple thing about it. Let's call it $C_{\mu\nu\lambda\sigma}$. This guy has to be symmetric in the two first indices \${\mu,\...