Vector Definition and 1000 Threads

As I understand it, the ratio of the electric field strength to the magnetic field strength at any point in a propagating electromagnetic plane wave is equal to the speed of light. How can the electric and magnetic field be perpendicular to each other yet still validate the E = cB equation? A...

Riley Hobson and Bence define covariant and contravariant bases in the following fashion for a position vector $$\textbf{r}(u_1, u_2, u_3)$$: $$\textbf{e}_i = \frac{\partial \textbf{r}}{\partial u^{i}} $$ And $$ \textbf{e}^i = \nabla u^{i} $$ In the primed...

Hi there. I wanted to ask this question, which is about efficiency in matrix times vector multiplication in fortran. When I have some matrix ##\hat A## and vector ##\vec{x}##, and I want to compute the matrix times vector ##\hat A \vec{x}=\vec{b}## in Fortran, what I do is, I build the array...

In the book, Introduction to Linear Algebra, Gilbert Strang says that every time we see a space of vectors, the zero vector will be included in it. I reckon that this is only the case if the plane passes through the origin. Else wise, how can a space contain a zero vector if it does not pass...

What is the mass of the lightest vector meson formed by bottom quarks and antiquarks?

So the main thing I'm wondering is given a question how do we determine whether to use one of the fundamentals theorems of vector calculus or just directly evaluate the integral, and if usage of one of the theorems is required how do we determine which one to use in the situation? Examples are...

Homework Statement I am trying to solve for change in velocity for the center of a rim with respect to the contact patch of a tire that has some degree of camber. The equation finalized is shown in the image below, equation 2.6. http://imgur.com/a/oHucp Homework EquationsThe Attempt at a...

I have always seen “vector” operators, such as the position operator ##\vec R##, defined as a triplet of three “coordinate” operators; e.g. ##\vec R = (X, Y, Z)##. Each of the latter being a bona fide operator, i.e. a self-adjoint linear mapping on the Hilbert space of states ##\mathcal H##. (I...

Homework Statement Homework Equations ##V=V^u \partial_u ## I am a bit confused with the notation used for the Lie Derivative of a vector field written as the commutator expression: Not using the commutator expression I have: ## (L_vU)^u = V^u \partial_u U^v - U^u\partial_u V^v## (1)...

A force F = -K(yi + xj) (K is a positive constant) acts on a particle moving in the x-y plane. Starting from the origin, the particle is taken along the positive x-axis to the point (a, 0) and then parallel to the y-axis to the point (a, a). What is the total work done by the force F on the...

Homework Statement Homework EquationsThe Attempt at a Solution [/B] A) Mean velocity is defined as <v> = total distance traveled/ total time taken = πR/Γ = 0.5 m/s B) How is part a) different from part b)? I think what Irodov means by mean velocity is mean speed in part a. It is mean...

I have posted this in University linear algebra, but it is possible there is a simple answer for this and the the problem belongs in some other forum. I apologize if that is the case. I am starting with 3 points in 3 space, along with the centroid of the full data set. The data is in principle...

Homework Statement Homework Equations The equation has already been given in the question. The Attempt at a Solution So what I did was find r'(t), r"(t), v(t), v'(t) and plug it into the equation. I've done 3 different full pages of this and have gotten 3 different answers. I'm guessing due...

Hi, In next semester, I am going to take vector calculus. Here is the course description: Vector fields, line and surface integrals, Green's Theorem, Stokes' Theorem, Divergence Theorem and advanced topics such as differential forms or applications to mechanics, fluid mechanics, or...

What is actually the unit normal vector of a surface? Is it this? Or this one? I see that those are opposite in direction. But, I want the correct one, which means that it should point outward. So, which one is correct?

Homework Statement Homework EquationsThe Attempt at a Solution [/B] Let ##k^u## denote the KVF. We have that along a geodesic ##K=k^uV_u## is constant , where ##V^u ## is the tangent vector to some affinely parameterised geodesic. ##k^u=\delta^u_i## , ##V^u=(\dot{t},\vec{\dot{x}})## so...

Hi, I would like to ask you how to properly describe the Feynman diagram of the Vector Boson Fusion where the Higgs boson is produced. Two quarks scatters two vector bosons (that means boson W or Z) at some moment which influence each other and produce the Higgs boson. Is that right...

I need help with 2.43 Is there any way to solve 2.43 without drawing the diagram again? And if I must draw another diagram, will I have to guess and check the length of the vectors since all the vectors are equal?

Homework Statement : [/B] r vector = 3t i + (4t-5t2)j. Find the angle made by the vector with respect to the x-axis and the y-axis. 2. Homework Equations : A.B=AxBx+AyBy 3. The Attempt at a Solution : I tried to take the dot product of the unit vector along x-axis and r. I did the same...

In the 1930s, John von Neumann consolidated ideas from Bohr, Heisenberg and Schrodinger and placed the new quantum theory in Hilbert space. In Hilbert space, a vector represents the Schrodinger wave function. I know they are equivalent.. But can we say it is more natural and intuitive to say...

I am confused why is space over field ##R## not over field ##C## ? The entries in each vector is an element of ##\Bbb C## not ##\Bbb R##.

Homework Statement A cricketer throws a 147g ball by exerting a force of 7.5N for 0.84s. If the launch angle is 39 degrees from horizontal, calculate the range of the ball. Homework EquationsThe Attempt at a Solution I have the range equation and I just need to find the magnitude of the...

Homework Statement Ex. 2. Express each of the following by an equation: (a) Two vectors A and B are parallel. (b) Three vectors A, B and C are co-planar. Homework Equations C = A + B 3. The Attempt at a Solution I understand (a) the answer being B = (alpha)*A because that is a scalar...

I am asking this because ∇ is also considered as a vector in some cases. Considering it as a vector in this case ,too, ( ∇× E).E = (- ∂ B/∂t).E = - ∂ (B.E)/∂t =0 Since B and E could be arbitrarily dependent on t, B.E = 0 where B and E are magnetic and electric fields respectively. This...

Homework Statement Suppose the position of an object is given by r⃗ = (3.0t2i^ - 6.0t3j^)m. Where t in seconds. Determine r⃗ at time t = 2.5 s. Express your answer using two significant figures. Express your answer in terms of the unit vectors i^ and j^. Homework Equations plugging in 2.5...

Homework Statement : [/B]Determine the resultant of three vectors of magnitude 1, 2 and 3 whose directions are those of sides of an equilateral triangle taken in order.Homework Equations : [/B] R2 = A2 + B2 + 2 A B cos θ tan α = B sin θ/(A+B cos θ) The Attempt at a Solution :[/B]...

Homework Statement Here are the three problems that i couldn't solve from the book Calculus volume 2 by apostol 10.9 Exercise 2. Find the amount of work done by the force f(x,y)=(x^2-y^2)i+2xyj in moving a particle (in a counter clockwise direction) once around the square bounded by the...

I have to do a teaching assistant job on a multivariable calculus class, I have to survey books that can be useful as resources. Has anyone used this book by Bourne and Kendall? I noticed that the treatment of vector analysis seems good and the chapter on Cartesian tensors seem to be a good...

Im learning about how to find the x and y components of a vector, but I wanted to verify if I'm on the right track.. Ax=A cos(\theta) <-- solving for x Ay=A sin(\theta) <-- solving for y So if a vector is 9.55m long and points in a -48.0 degree direction. Is it Ay= 9.55 sin(-48.0)=7.3

Homework Statement Show that the normal derivative of the coulomb gauge vector suffers a jump discontinuity at a surface endowed with a current density K(\vec r_s ) Homework Equations The vector potential A is given by: A=\frac{\mu_0}{4\pi}\int{\frac{J(x')}{|x-x'|}d^3x} The magnetic...

Hi. I was investigating through this week why there are the differential forms, why are they anti-symmetric, why do we have the Jacobian when expressing the volume in a different coordinate system. This was just fantastic! I found all the connections between these topics. And I found that all of...

Why is the dot product equivalent to the matrix multiplication of its components? I've seen some proofs using Pythagorean and cosine law but they don't give you an intuitive feel as to why matrix multiplication works. The geometric definition (##ab cosθ##) is very easy to understand. To a...

Homework Statement Let L1 be the tangent line to r(t) at the point t = a and let L2 be the tangent line where t = b. Find the equation of the lines L1. Find the equation of the lines L1 and L2 and find the points of intersection. r(t) = <f(t), g(t), h(t)> *bolded letters are vectors Homework...

Hello! I read this definition of vectors in my GR book: "To each point p in spacetime we associate the set of all possible vectors located at that point; this set is known as the tangent space at p, or ##T_p##". This means that each point in space time is viewed as the origin for the 4...

I'm working on a school project and my goal is to recognize objects. I started with taking pictures, applying various filters and doing boundary tracing. Fourier descriptors are to high for me, so I started approximating polygons from my List of Points. Now I have to match those polygons, which...

The basic idea: I am interested in the possibility of an azimuthally-directed Poynting vector component which drops with the inverse cube of the distance (or as 1/r^3), primarily because it suggests the possibility of emitting field angular momentum, allowing for a uni-directional torque to be...

Homework Statement (Picture attached) Question 1: The system starts at rest. Block a accelerates towards the bottom the the rod. Find the velocity of the block when it is at the bottom of the rod using the "vector method". So this was my midterm question today. I knew how to figure out how...

Hi guys, I am a little confused on the difference between an Algebra and a vector space. I´m guessing there´s a fairly simple distinction. Any guidance would be much appreciated, I accept both hand wavy and hardcore axiom based responses :) Cheers

1. There is a function f(x). Write regulations for it if: -you move it by a vector r=(a,b), -you mirror it over x or y axis.2. f(x) isn't exactly given. Vector is r(a,b).3. If we move it by vector: f(x-a)+b, If we mirror it over x: -f(x) If we mirror it over y: f(-x) So if I am correct...

Relations between vectors in cylindrical and Cartesian coordinate systems are given by \vec{e}_{\rho}=\cos \varphi \vec{e}_x+\sin \varphi \vec{e}_y \vec{e}_{\varphi}=-\sin \varphi \vec{e}_x+\cos \varphi \vec{e}_y \vec{e}_z=\vec{e}_z We can write this in form \begin{bmatrix}...

Homework Statement Two spheres, with 0.5g each, are hanging by 30cm threads, tied on the same spot. The same electric charge is communicated to each sphere; in consequence, the threads move apart until they are about 60^\circ from each other. What is the value of the charge? \theta =...

Homework Statement Find the general solution to the equation: ##{u}\times{(i+4j)}=3k## Homework Equations ##u=(ai+bj+ck)## The Attempt at a Solution I am having trouble visualising what to do here. So my throught so far is that, if i do ##(ai+bj+ck)\times {(i+4j)}=(0i-0j+(4a-b)k) ## now if I...

<Mentor's note: moved from general mathematics to homework. Thus no template.> Prove subspace is only a subset of vector space but not a vector space itself. Even a subspace follows closed under addition or closed under multiplication,however it is not necessary to follow other 8 axioms in...

L1 [x,y]=[2,1]+r[-5,1] L2 [x,y]=[1,4]+s[2,1] L3 [x,y]=[3,5]+t[4,-5] These three lines are sides of a triangle find: 1)the perimeter of the triangle 2) The largest angle 3) the centroid of the triangle so I converted the vector equations into parametric, and then made two of the x parametric...

Homework Statement Hi guys, I have am having a problem with the questions below. what do they mean by show ## B_{perp}=B sin\theta ## I mean I know it a silly question, and my first thought is just use socahtoa, or am I missing something. The question from there on is straight forward...

There is a problem in my Physics textbook which says: Homework Statement "A car runs counter-clockwise in a circular lane of 1 km of diameter, going through the south extreme at 60 km/h on the instant t = 0. From that point onwards, the driver accelerates the car uniformely, reaching 240 km/h...

Excuse me if this is a bad question but: Does ##d P_x d P_y = d^2 \vec P ##? I thought not because ##P_x ## is a scalar , a component of the vector, whereas ##\vec P ## is a vector? Thanks in advance

Hello, I am trying to understand how vector images are formed and manage to be scaled up or down without distortion. Bitmap images are easy: they are a grid of pixels and each pixel has a certain color. Scaling a bitmap image of 10x10 pixels implies adding new extra pixels and using...

Homework Statement http://imgur.com/a/k7fwG Find the vector magnetic potential at point P1. Homework Equations Vector magnetic potential given by: $$ d \bar{A} = \frac{\mu I d\bar{l'}}{4 \pi | \bar{r} - \bar{r'} | } $$ The Attempt at a Solution I split up the problem in 3 parts, first...

1. Problem ##g_{uv}'=g_{uv}+\nabla_v C_u+\nabla_u C_v## If ##g_{uv}' ## is given by ##ds^2=dx^2+2\epsilon f'(y) dx dy + dy^2## And ##g_{uv}## is given by ##ds^2=dx^2+dy^2##, Show that ## C_u=2\epsilon(f(y),0)##? Homework Equations Since we are in flatspace we have ##g_{uv}'=g_{uv}+\partial_v...