What is Vector: Definition and 1000 Discussions

This is probably a stupid question, but I have never realised that there's an order things should be done in the chain rule , so for example ## \nabla(\bf{v}.\bf{v})=2\bf{v} (\nabla\cdot \bf{v}) ## and not ## 2 \bf{v} \cdot \nabla \bf{v} ## Is there an obvious way to see / think of this...

For this problem, Is the length vector into or out of the page and how do you tell? EDIT: Why must we use conservation of energy for this problem? I tried solving it like this: ##IdB\sin90 = ma ## ##IdB = ma ## ##v_f = (2aL)^{1/2} ## ##v_f = (\frac {2dIBL} {m})^{1/2} ## Which is incorrect...

I refer to the video of this page, where there is a description of Galilean relativity that is meant to be an introduction to SR, making the comprehension of the latter easier as a smooth evolution from the former. All the series is in my opinion excellent, but I think that this aspect is...

I tried using the distance between r2 and r1 and plugging them into the equation for i, j, k. >> So for the force in the x direction it was k*(4E-6*4E-6)/(4-9)^2. The answer I got was wrong according to webassign. Can someone please tell me what I am missing?

This is an international past paper question- I have attached the question and the markscheme... the ms was a bit confusing for 2 marks hence my post. Question; interest is on part iii. only Mark scheme solution; My thinking; Let ##OD=λOA## Where ##λ## is a scalar. ##OD=λ...

TL;DR Summary: My problems comes to a vector expression which needs to be simplified I got an expression pi=εijksk,lul,j Here s and u are two vectors. What will be the vector expression of this vector p with curl s, curl u, and other operations?

Given vector operators as $$\mathbf{A} = (A_{1}, A_{2} ,A_{3}) $$ $$\mathbf{B} = (B_{1}, B_{2} ,B_{3}) $$ $$\mathbf{C} = (C_{1}, C_{2} ,C_{3}) $$ I know that for two vector operators $$\begin{equation} \mathbf{Q} \mathbf{P} = \sum_{\alpha = 1}^{3} Q_{\alpha} P_{\alpha} \end{equation}$$...

when you do a multipole expansion of the vector potential you get a monopole, dipole, quadrupole and so on terms. The monopole term for a current loop is μI/4πr*∫dl’ which goes to 0 as the integral is over a closed loop. I am kinda confused on that as evaulating the integral gives the arc length...

Hi I was just wondering about the suvat formulae and a question popped into my head, which I'd like someone to try and explain the reason as to why please. So I know that when we have a formula such as F=ma or v = u + at, you can evaluate the magnitude of both sides and arrive at a scalar...

##f\left(x\right)=\begin{cases}\sqrt{\left|xy\right|}sin\left(\frac{1}{xy}\right)&xy\ne 0\\ 0&xy=0\end{cases}## I showed it partial derivatives exist at ##(0,0)##, also it is continuous as ##(0,0)## but now I have to show if it differentiable or not at ##(0,0)##. According to answers it is not...

1. To find the solution simply integrate the e_r section by dr. $$\nabla g = A$$ $$g = \int 3r^2sin v dr = r^3sinv + f(v)$$ Then integrate the e_v section similarly: $$g = \int r^3cosv dv = r^3sinv + f(r)$$ From these we can see that ##g = r^3sinv + C## But the answer is apparently that there...

How do I calculate the unit normal vector for any metric tensor?

Hi, there. I am currently reading the paper, Gravitational Faraday rotation induced by a Kerr black hole (https://doi.org/10.1103/PhysRevD.38.472). After Eq. (2.4), it reads that The paper does not provide the derivation of the equations and no related reference is listed. Also, ##k^i## is not...

Normalize function f(r) = Nexp{-alpha*r} Where alpha is positive const and r is a vector I was just wondering if the fact that we have a vector value in our equation changes anything about the solution

Hi, the task is as follows Unfortunately, I am not getting anywhere at all with task c. I have now proceeded as follows: I assume that the calculation takes place in the reference system of the sun. In the task the following is valid, $$\vec{v}_{si}=-s\vec{v}_p$$ I have now simply assumed...

Hello everyone, I was looking at the light matter interaction Hamiltonian and I worked out a simple calculation where I was surprised to see that I had to introduce an explicitly non-local vector potential if I want to go further: $$\langle\psi|...

Hi, For a 2 x 2 matrix ##A## representing a Markov transitional probability, we can compute the stationary vector ##x## from the relation $$Ax=x$$ But can we compute ##A## of the 2x2 matrix if we know the stationary vector ##x##? The matrix has 4 unknowns we should have 4 equations; so for a ##A...

vector subtraction of ppl is simple but i cant visualise the subtraction please help

TL;DR Summary: Looking for literature on O(N) vector model Hello, We have been going over the O(N) vector model in my QFT class but the notes are not very detailed and we are not using a textbook. Does anyone know of a good QFT book which goes over this material? I have a copy of Shrednicki...

As an example, consider a vector-valued function of the form ##f(x,y) = (g_1(x,y),g_2(x,y))##. I typed up one example on wolfram to see if this could be visualized https://www.wolframalpha.com/input?i=plot+f(x,y)+=+(x+y,xy) which was inspired by this question...

Suppose M is a manifold and $$T_{p}M$$ is the tangent space at a point $$p \in M$$. How do i prove that it is indeed a vector space using the axioms: Suppose that u,v, w $$\in V$$. where u,v, w are vectors and $$\V$$ is a vector space $$u + v \in V \tag{Closure under addition}$$ $$u + v = v +...

This might seem like a novice question, but let's suppose we have a vector ##x## and we want to turn it into vector ##y##. Well, what square matrix multiplied on ##x## accomplishes this? As an example, let's work with a ##2 \times2## case: ##x = \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}## and...

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here i found AB to be (-3, 2) and then i thought to do 2/5 multiplied by AB to find AC, however this is incorrect and instead i would have to involve the origin. Why and how can i involve the origin?

for 3di i did the normal AB=BC so b-a would give either satisfy or not this phenomenon, my answer was (3a-1, -4) & (2a^2 + a - 1, 4a - 2), now how would i know from here if they're collinear or not?

I know what x and y components are but this is really confusing me. And the angle I think is the inverse of tan something. part 3 is so confusing smh

I was thinking of using the chain rule with dF/dx = 0i + (3xsin(3x) - cos(3x))j and dF/dy = 0i + 0j but dF/dy is still a vector so how can it be inverted to get dy/dF ? what are the other methods to calculate this?

Let C2x2 be the complex vector space of 2x2 matrices with complex entries. Let and let T be the linear operator onC2x2 defined by T(A) = BA. What is the rank of T? Can you describe T2? ____________________________________________________________ An ordered basis for C2x2 is: I don't...

Good Morning! I understand that a vector is a physical object I understand that it is the underlying basis that determines how the components transform. However, I encounter this: https://en.wikipedia.org/wiki/Covariance_and_contravariance_of_vectors The fifth paragraph has this statement A...

Hello! I'm trying to understand how this pendulum works. I found this video that explains how to calculate the T force from the rope. He uses the preservation of kinetic and potential energy in order to find the magnitude of the velocity and then using Newton's second law, he calculates the T...

Here is my attempt (Note: ## \left| \int_{C} f \left( z \right) \, dz \right| \leq \left| \int_C udx -vdy +ivdx +iudy \right|## ##= \left| \int_{C} \left( u+iv, -v +iu \right) \cdot \left(dx, dy \right) \right| ## Here I am going to surround the above expression with another set of...

The answer is (B) but I don't understand why (C) is wrong. The force acting on the hinge has two components, horizontal and vertical. The horizontal component must be to the right to balance the horizontal component of tension but the vertical component can be either upwards or downwards. Wow to...

The magnitude of cross product is defined of vector A⃗ and B⃗ as |A⃗×B⃗|=|A⃗||B⃗|sinθ where θ is defined as the angle between the two vector and 0≤θ≤π.the domain of θ is defined 0≤θ≤π so that the value of sinθ remains positive and thus the value of the magnitude |A⃗||B⃗|sinθ also remain positive...

Definition of linear operator in quantum mechanics "A linear operator ##A## associates with every ket ##|\psi\rangle \in \mathcal{E}## another ket ##\left|\psi^{'}\right\rangle \in\mathcal{E}##, the correspondence being linear" We also have vector operators ##\hat{A}## (such as a position...

I know the normal of plane ABQP is -2i - j + 3k but I don't know how to prove that 2i + j + 3k is the normal vector of plane CDPQ Thanks

hi guys I am trying to learn special relativity and relativistic quantum mechanics on my own and just very confused about the different conventions used for the notation!?, e.g: the four position 4-vector some times denoted as $$ x_{\mu}=(ct,-\vec{r})\;\;or\;as\;x_{\mu}=(ict,\vec{r}) $$ or...

The vectorfield is $$A = grad \Phi$$ $$A = x^2 + y^2 + z^2 - (x^4 + y^4 + z^4 + 2x^2y^2 + 2x^2z^2 + 2y^2z^2)$$ The surface with maximum flux is the same as the volume of maximum divergence, thus: $$div A = 6 - 20(x^2 + y^2 + z^2)$$ This would suggest at the point 0,0,0 the flux is at maximum...

There is a passage in this book where I don't follow the logic; In this short quotation from 'Quantum Mechanics: The Theoretical Minimum' by Leonard Susskind and Art Friedman \mathcal{A} represents the apparatus that is performing the measurement the apparatus can be oriented (in principle) in...

what would be the y'-x' ##\vec r## vector be? I think it is ##\vec r = (8t - 1) \hat i + (6t - 2) \hat j## (not sure whether it is correct or not.) I thought about it as at t = 0 the position needs to be -1i -2j so that is why I took the signs in the y'-x' frame position vector as a - instead...

I am trying to derive radial and axial magnetic fields of a current carrying loop from its magnetic vector potential. So far, I have succeeded in deriving the radial field but axial field derivation gives me trouble. My derivation of radial field (eq 1) can be found here. Can anyone point out...

A golf is launched at a speed v,f and launch angle, β,f. The slope of the green is equal to φ. At some point the ball is located on the rim of a hole. The side view (a) and overhead view (b) looks as in the attached image.According to the author of the [paper][2] "The Physics of Putting" the...

##f : [0,2] \to R##. ##f## is continuous and is defined as follows: $$ f = ax^2 + bx ~~~~\text{ if x belongs to [0,1]}$$ $$ f(x)= Ax^3 + Bx^2 + Cx +D ~~~~\text{if x belongs to [1,2]}$$ ##V = \text{space of all such f}## What would the basis for V? Well, for ##x \in [0,1]## the basis for ##V##...

(1,1)or(2,0)or(0,2)?And does a dual vector field have gradient?

N/A

Hello! I have this system here $$ \left[ \begin{matrix} -2 & 4 & \\\ 1 & -2 & {} \end{matrix} \right]x +\begin{pmatrix} 2 \\\ y \end{pmatrix}u $$ Now although the problem is for my control theory class,the background is completely math(as is 90% of control theory) Basically what I need to...

If we define Laplacian of scalar field in some curvilinear coordinates ## \Delta U## could we then just say what ##\Delta## is in that orthogonal coordinates and then act with the same operator on the vector field ## \Delta \vec{A}##?

I have been trying to determine an expression for a unit vector in the direction of F for hours now. I think the expression is supposed to look something kind of like this, But I don't understand at all how to arrive at this expression. Any help?

...and is it ever useful? An arbitrary complex number has the form ##z = a + bi## where ##a, b \in \mathbb{R}## and the dot product of two arbitrary vectors ##\vec{v} = \binom{v_1}{v_2}## and equivalently for vector ##\vec{w}## is ##\vec{v} \cdot \vec{w} = v_1 w_1 + v_2 w_3## Then the ##z## may...

Good afternoon everyone, I have a question on Newton's 2nd Law regarding objects on a generic incline. Take for example, a car on a banked curve: Here in the picture I've provided, you can see that the normal force has been decomposed into the x and y components via sine and cosine of the...