What is Vector: Definition and 1000 Discussions

Hi I found this paper on the measurement of unknown velocity vector of a closed space. Does it mean that it is possible to measure the unknown velocity vector of a closed space ? Can someone explain it to me

The first thing I did, was to find the equations for player A (p) and ball's (b) path (for each i and j component I used the equation I wrote in the relevant equations) and then I found the derivative of both equations so I could have the velocity: $$\vec{r}_p(t)=(6t^2+3t)\hat{i}+20\hat{j}...

Summary:: the set of arrays of real numbers (a11, a21, a12, a22), addition and scalar multiplication defined by ; determine whether the set is a vector space; associative law Question: determine whether the set is a vector space. The answer in the solution books I found online says that...

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Hi, I just have a quick question about a problem involving Gauss' Theorem. Question: Vector field F = \begin{pmatrix} x^2 \\ 2y^2 \\ 3z \end{pmatrix} has net out flux of 4 \pi for a unit sphere centred at the origin (calculated in earlier part of question). If we are now given a vector...

Hello, I am after some help to try and understand SVM implementation is a micro that controls a motor. As I understand it one of the advantages of using space vector modulation over sinusoidal PWM modulation in motor control is that it can control the phase voltages such that the line-to-line...

r_{13}=r_{23}=\sqrt{(30*10^{-3})^2+(90*10^{-3})^2}=\sqrt{9*10^{-3}}\\ F^E_{13}=F^E_{23}=9E9\cdot\frac{5*10^{-9}\cdot3*10^{-9}}{9*10^{-3}}=1.5*10^{-5}\\ \theta=tan^{-1}(\frac{90*10^{-3}}{30*10^{-3}})=71.565\,degrees\\ \vec{F}^E_{13}=<F^E_{13}cos\theta, F^E_{13}sin\theta> = <4.743*10^{-6}...

The velocity of a particle below is expressed in polar coordinates, with bases e r and e theta. I know that the length of a vector expressed in i,j,k is the square of its components. But here er and e theta are not i,j,k. Plus they are changing as well. Can someone help convince me that the...

Denote ##v=(1,2,3)^T##, ##\theta=\arctan(2)##, and ##\phi=\arctan(\frac{3}{\sqrt{5}})##.The way that I attempted this was by performing the following steps: (1) Rotate ##v## about the z-axis ##-\theta## degrees, while keeping the z-coordinate constant. (2) Rotate ##v## about the y-axis...

I'm going through the "Advanced Lectures on General Relativity" by G. Compère and got stuck with solving one set of conditions on the subject of asymptotic flatness. Let ##(M,g)## be ##4##-dimensional spacetime and ##(u,r,x^A)## be a chart such that the coordinate expression of ##g## is in Bondi...

I have been at this exercise for the past two days now, and I finally decided to get some help. I am learning General Relativity using Carrolls Spacetime and Geometry on my own, so I can't really ask a tutor or something. I think I have a solution, but I am really unsure about it and I found 6...

How do we verify whether a condition on the magnetic vector potential A constitutes a possible gauge choice ? Specifically, could a relation in the form A x F(r,t) be a gauge , where F is an arbitrary vector field?

Hi, I've been stuck for a long time with this exercise. I am not able to calculate the potential vector, since I do not know very well how to pose the itegral, or how to decompose the disk to facilitate the resolution of the problem. I know that because the potential vector must be parallel to...

We have a retarded magnetic vector potential ##\mathbf{A}(\mathbf{r},t) = \dfrac{\mu_0}{4\pi} \int \dfrac{\mathbf{J}(\mathbf{r}',t_r)}{|\mathbf{r}-\mathbf{r}'|} \mathrm{d}^3 \mathbf{r}'## And its curl, ##\mathbf{B}(\mathbf{r}, t) = \frac{\mu_0}{4 \pi} \int \left[\frac{\mathbf{J}(\mathbf{r}'...

I know there is an identity involving the Laplacian that is like ##\nabla^2 \vec A = \nabla^2 A## where ##\vec A## is a vector and ##A## is its magnitude, but can't remember the correct form. Does anyone knows it?

The moving magnet and conductor problem is an intriguing early 20th century electromagnetics scenario famously cited by Einstein in his seminal 1905 special relativity paper. In the magnet's frame, there's the vector field (v × B), the velocity of the ring conductor crossed with the B-field of...

Summary:: Seeding and visualization techniques Hi I am looking for resources where I can learn the following: Seeding strategies and algorithms for vector fields (texture-based, geometry, topological) Different techniques for visualizing vector fields (streamlines, glyph-based, LIC etc)

I am trying to understand the following derivation in my lecture notes. Given an n-dimensional manifold ##M## and a parametrized curve ##\gamma : (-\epsilon, \epsilon) \rightarrow M : t \mapsto \gamma(t)##, with ##\gamma(0) = \mathbf{P} \in M##. Also define an arbitrary (dummy) scalar field...

Hi, I'm trying to find the magnetic field B using F = qV * B. I have F = (3i + j + 2k) N V = (-i +3j) * 10^6 m/s q = -2 *10^6 C Bx = 0 I don't know how to resolve a 3 dimensional vector equation. B = F/qV makes not sense for me.

Hi! My first question: How does he get the equation ##\frac {x_A} {2πr_1} = -\frac {θ} {2π}## ?

Hello all, In high school physics, the magnitude sum of vector addition can be found by cosine rule: $$\vec {R^2} = \vec {F^2_1} + \vec {F^2_2} + 2 \cdot \vec F_1 \cdot \vec F_2 \cdot cos ~ \alpha$$ and its angle are calculated by sine rule: $$\frac {\vec R} {sin ~ \alpha} = \frac {\vec F_1}...

Hey! :o We have the vectors $v=i+j+2k=(1,1,2)$ and $u=-i-k=(-1,0,-1)$. I have calculated the following: \begin{align*}&|v|=\sqrt{1^2+1^2+2^2}=\sqrt{1+1+4}=\sqrt{6} \\ &|u|=\sqrt{(-1)^2+0^2+(-1)^2}=\sqrt{1+0+1}=\sqrt{2} \\ &v\cdot u=(1,1,2)\cdot (-1,0,-1)=1\cdot (-1)+1\cdot 0+2\cdot...

Summary:: I'm quite stuck on this problem i don't know what I am going to use formula to solve this one This is the given I am not sure if this is a resolution problem or it involve parallelogram law

I do not understand how can I parameterize the surface and area and line differentials.

Homework Statement:: F is not conservative because D is not simply connected Relevant Equations:: Theory Having a set which is not simply connected is a sufficient conditiond for a vector field to be not conservative?

The energy is the 0-th component of the four momentum vector ##p^\alpha##. How is called the component ##p_0 = g_{0\alpha}p^\alpha##?

Hi, This feels like such a stupid question, but it's bugging me. Two displacements can be represented with two vectors. Let's say their magnitudes are expressed in metres. The scalar (dot) product of the two vectors results in a value with the units of square metres, which must be an area. Can...

let ##f : R^3 → R## the function ##f(x,y,z)=(\frac {x^3} {3} +y^2 z)## let ##\gamma## :[0,## \pi ##] ##\rightarrow## ##R^3## the curve ##\gamma (t)##(cos t, t cos t, t + sin t) oriented in the direction of increasing t. The work along ##\gamma## of the vector field F=##\nabla f## is: what i...

My idea is to evaluate it using gauss theorem/divergence theorem. so the divergence would be ## divF = (\cos (2x)2+2y+2-2z ( y+\cos (2x)+3) ) ## is it correct? In this way i'ma able to compute a triple integral on the volume given by the domain ## D = \left\{ (x, y, z) ∈ R^3 : x^2 + y^2 +...

Hello! I am reading about spin-orbit coupling in Griffiths book, and at a point he shows an image (section 6.4.1) of the vectors L and S coupled together to give J (figure 6.10) and he says that L and S precess rapidly around J. I am not totally sure I understand this. I know that in the...

Summary:: Suppose that [x, y] = e^{-3t} [-2, -1] is a solution to the system $x' = Ax$, where A is a matrix with constant entries. Which of the following must be true? a. -3 is an eigenvalue of A. b. [4, 2] is an eigenvector of A. c. The trajectory of this solution in the phase plane with axes...

I've attached a .txt file of my script for those who want to take a look at it Here's a picture of my vector field at time t = 0 I'm very concerned about this picture because from my understanding the Poynting vector is supposed to point outwards and not loop back around, this looks nothing...

is it correct if i use Gauss divergence theorem, computing the divergence of the vector filed, that is : div F =2z then parametrising with cylindrical coordinates ##x=rcos\alpha## ##y=rsin\alpha## z=t 1≤r≤2 0≤##\theta##≤2π 0≤t≤4 ##\int_{0}^{2\pi} \int_{0}^{2} \int_{0}^{4} 2tr \, dt \, dr...

Given ##F (x, y, z) = (0, z, y)## and the surface ## \Sigma = (x,y,z)∈R^3 : x=2 y^2 z^2, 0≤y≤2, 0≤z≤1## i have parametrised as follows ##\begin{cases} x=2u^2v^2\\ y=u\\ z=v\\ \end{cases}## now I find the normal vector in the following way ##\begin{vmatrix} i & j & k \\ \frac {\partial x}...

I need to prove this using the given equations. $$\vec{N}(t) = \frac{\vec{a}_{v\perp}}{|\vec{a}_{v\perp}|}$$ Here is the entirety of my work up to this point. So far I've wanted to use what I have to find something that is perpendicular to the velocity vector and maybe show that with the dot...

For a specific wave vector, ##k##, the group of wave vector is defined as all the space group operations that leave ##k## invariant or turn it into ##k+K_m## where ##K_m## is a reciprocal vector. How the translation parts of the space group, ##\tau##, can act on wave vector? Better to say, the...

I'm struggling to get the hang of killing vectors. I ran across a statement that said energy in special relativity with respect to a time translation Killing field ##\xi^{a}## is: $$E = -P_a\xi^{a}$$ What exactly does that mean? Can someone clarify to me?

Hi, My question pertains to the question in the image attached. My current method: Part (a) of the question was to state what Stokes' theorem was, so I am assuming that this part is using Stokes' Theorem in some way, but I fail to see all the steps. I noted that \nabla \times \vec F = \nabla...

I understand that the Dual Space is composed of elements that linearly map the elements of the Vector Space onto Real numbers If my preamble shows that I have understood correctly the basic premise, I have one or two questions that I am trying to work through. So: 1: Is there a one to one...

Hello, I start by applying the integral for the vector potential ##\vec{A}## using cylindrical coordinates. I define ##r## as the distance to the ##z##-axis. This gives me the following integral,$$\vec{A} = \frac{\mu_0}{4\pi} \sigma_0 v 2 \pi \hat{x} \int_0^{\sqrt{(ct)^2-z^2}}...

I am so confused.If F and d are both vector quantity.How come W is a scalar quantity?

I am trying to understand “divergence” by considering a one-dimensional example of the vector y defined by: . the parabola: y = -1 + x^2 The direction of the vector y will either be to the right ( R) when y is positive or to the Left (L). The gradient = dy/dx = Divergence = Div y = 2 x x...

I don't know which part gets wrong

vector=(abc) 1. $$\begin{pmatrix} 1 & 0 & 0 \\ 0 & cos(\theta) & -sin(\theta) \\ 0& sin(\theta) & cos(\theta) \end{pmatrix}$$ The rotation part is correct. 2. $$\begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0& 0 & 0 \end{pmatrix}$$ is wrong apparently how do I do the mirroring? step 3 i can do...