# Tag Info

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### How can I reproduce a beautiful 3D vector plot?

Nice "inverse problem". The angle distribution looks to me like a Gaussian. ...
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### Visualizing gravity warping the fabric of spacetime

Here my physicist approach to the problem: I consider a cloud/grid of test-particles which get attracted to a reference point by a force. In the following I assume attraction by gravity -- i.e. the ...
• 3,410
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### Animate a circle "rolling" along a complicated 3D curve

EDIT As OP wishes (and as Rahul correctly points out) my original answer puts unit circle in TB plane (my error as labels suggest) and what is desired is TN plane. ...
• 62.1k
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### Remove Abs from Norms of Vectors

expr = Norm[{a, b*c}] Sqrt[Abs[a]^2 + Abs[b c]^2] Since ComplexExpand assumes all its variables to be real, we ...
• 7,870

### How can I reliably plot ellipse-field streamlines?

Use NDSolve to solve for y(x) Perhaps this serves as a starting point. Shown below is the case when b = -1. Each streamline is obtained from ...
• 5,279
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### Speeding up cross and dot products for a list of vectors

Almost the fastest way would be to use Compile to generate a CompiledFunction. ...

### Vectors with a certain magnitude in Mathematica

RandomPoint makes this a one liner (as of version 10.2): RandomPoint[Sphere[{0, 0, 0}, 4]] ...
• 36.4k
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### stream plot 2d cross section

You may use SliceVectorPlot3D. ...
• 42.4k

### How do I determine if two 2d vector parallel?

Based on the definition of the scalar product for $d$-dimensional vectos $$a \cdot b = |a| |b| \cos(\phi)$$ you can create a test based only on vector operations. The ...
• 5,483
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### Can we turn this for loop into a more elegant Mathematica code?

Apparently, you try to apply a permutation given by list indirection to a vector duplicate. Here are several ways to do it, ...

### How do I sum the products of the elements of a vector?

SymmetricPolynomial is the built-in way to get the sums you want: ...
• 41.9k

### Remove Abs from Norms of Vectors

If you have to use FullSimplify or Simplify, you can use the option ComplexityFunction to ...
• 398k

### How to show a time-dependent vector (velocity) with Manipulate?

You can do it thus: Manipulate[ Show[trayectoria, Graphics3D[Arrow[{pos, pos + vel} /. t -> α]]], {α, 0, 10 Pi}]
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### How to show a time-dependent vector (velocity) with Manipulate?

By defining your kinematics equations as top-level expressions (rather than as functions of the relevant quantities), you invite scoping problems. I recommend working with functions and making the <...
• 108k

### Dot Product and Simplification

You'll want to use TensorReduce or TensorExpand with appropriate assumptions for reducing expressions involving ...
• 9,020
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### How do I determine if two 2d vector parallel?

$a$ and $b$ are parallel if $a = \kappa b$. Try MatrixRank[{a, b}] == 1 for an easy way to test this. This works only if neither of the vectors have norm ...
• 236k
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### What is the operator **?

Since this was missing from What are the most common pitfalls awaiting new users? I'll answer. ** is shorthand for ...
• 272k
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### Exporting 2D projection of 3D graph in SVG form

In principle, this all is not difficult but there are some obstacles in the way that will make life hard: In a 2d projection of a 3d polygon graphics, many of the polygons are not visible since they ...
• 113k
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### How to simplify tensor expression with symbolic coeficients?

\$Assumptions = {(a | b | c) ∈ Vectors[3], g ∈ Reals} TensorReduce[g b.a\[Cross]c - g c.b\[Cross]a] 0
• 398k
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### Multiplying list of matrices with vector of scalars

An easy way to achieve this, is to use Inner with a level specification. In this case, you want the inner product to work only on the first level: ...
• 23.8k

### Summation of Kronecker deltas should give the dimension

You could just do: Sum[KroneckerDelta[μ, ν] KroneckerDelta[μ, ν], {ν, d}, {μ, d}, Assumptions->d>1] d Although it might make sense to use symbolic ...
• 131k
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### 3D Vectors wrap on the Sphere

Create a mesh ...
• 19.1k
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### 3d Vector Wrap of Half sphere

The lighting is a bit hard to get right without ray-tracing (though possible in Mathematica on Mac). Here is a first attempt, feel free to improve. ...
• 3,448
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### Mimicking Günther Uecker's nail art

Just an idea about using VectorPlot3D with a custom nail marker: ...
• 4,961

### How to create an array from all combinations of the vector components?

Try Flatten[Outer[{#1, #2} &, {a, b, c}, {w, x, y, z} ], 1] (*{{a, w}, {a, x}, {a, y}, {a, z}, {b, w}, {b, x}, {b, y}, {b, z},{c,w}, {c, x}, {c, y}, {c, z}}*)
• 54.6k
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### multiplication of vector spaces

Here's a take that allows one to keep track of the order of things carefully. Note that this is similar in nature to the answer here. Annihilation operators We first construct the annihilation ...
• 23.9k
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### Divide column of a matrix by a specific number

de[[All, 2]] /= 2; de Or if you can't replace the old values deNew = de; deNew[[All, 2]] /= 2; deNew
• 20.3k