What is Vector: Definition and 1000 Discussions

Homework Statement A vector field is pointed along the z-axis, v → = a/(x^2 + y^2)z . (a) Find the flux of the vector field through a rectangle in the xy-plane between a < x < b and c < y < d . (b) Do the same through a rectangle in the yz-plane between a < z < b and c < y < d . (Leave your...

In the four-observation method of Gauss for orbit determination, the right ascension and declination of an asteroid is observed at specified times, and the heliocentric position of Earth is obtained from tables (or JPL Horizons) for those same times. I can follow the procedure to the point...

How do I calculate the resultant of three component vectors set mutually at 60 degrees to each other (not in the same plane)?

Homework Statement Hi. Its not really a problem but just a general question. When doing graph translations, such as move the parabola x units right or y units up etc, Is it okay to use vector format. So instead of saying move this equation 4 units left, could you write it like this -> <-4,0>...

Homework Statement A force of magnitude 50N is applied at the bottom point Q of a disk of radius 8m that is pinned at P (leftŸmost point) See attached picture (a) Find the angle between the force and the vector from P to Q. (b) Find the magnitude of the applied torque. Homework Equations...

Can we say that a volume element can be represented by a vector, or is there some hidden complication that makes this inadvisable? For some background, the stress-energy tensor has been described as the density of energy and momentum, in for instance MTW. So if one says that the represention...

How to draw the following vector field: F(r) = 1/(r^2) I know the shape of this vector field and how to draw a vector field in terms of x- and y-components, but I was wondering how to draw a vector field in terms of a vector r, as given above, without knowing its components. Any advice is much...

If W is a skew-symmetric tensor, (i) Write down the most general form of [W]e. (ii) Show that there exist a vector w in R3 such that Wx = w*x for each x in R3. Such a vector w is called the axial vector of W. (iii) Use part (ii) to deduce that x.Wx = 0 for any x in R3. (iv) If W has axial vector...

Equation 9.2.25 defines the inner product of two vectors in terms of their components in the same basis. In equation 9.2.32, the basis of ## |V \rangle## is not given. ## |1 \rangle ## and ## |2 \rangle ## themselves form basis vectors. Then how can one calculate ## \langle 1| V \rangle ## ? Do...

Hey, I've got this problem that I'm trying to work out. I've tried a couple of things, but they don't really get me anywhere. Here's the problem Find a vector that spans the line defined by these two equations. $x+6y+3z=0$ $x+3y+4z=0$ What would be the best way to go about this? Thanks :)

Hi PF! Given a vector field ##\vec f## in spherical coordinates as a function of a single parameter ##s##, shown here as $$\vec f(s) = f_r(s) \hat r + f_\theta(s) \hat \theta + f_\phi(s) \hat\phi$$ where here subscripts do not denote partial derivatives, but instead are used to define...

Homework Statement https://www.physicsforums.com/attachments/229290 Homework Equations The Attempt at a Solution I am not sure what equation to use for the volume[/B]

Homework Statement f f Homework Equations ##a = {v^2}{r}## ##d = vt## The Attempt at a Solution The way I do it is break it down into the curved and straight segment. The bicycle is always traveling at a constant speed. Curved portion: distance ##\frac{\pi R^2}{4}## acceleration ##=...

Can we find the angle between resultant and one of its vectors without breaking into components?

Homework Statement 1.1.3 1) Do functions that vanish at the endpoints x=0 and L=0 form a vector space? 2) How about periodic functions? obeying f(0)=f(L) ? 3) How about functions that obey f(0)=4 ? If the functions do not qualify, list what go wrong.Homework Equations The Attempt at a...

Homework Statement Homework Equations definition of null vector, [/B] The Attempt at a Solution null vector : ## |0 \rangle = (0,0,0) ## inverse of (a,b,c) = ( - a, -b, -c) vector sum of the two vectors of the same form e.g. (c,d,1) + ( e,f,1) = ( c+e, d+f, 2) does not have the same...

For the vector valud function F in the image, the three components of the output vector at a point are functions of (x,y,z)the three coordinates of the point.But while calculating divergence, why is the rate of change of x component of the output along x direction alone is accounted(similarly...

Would you explain this sentence in detail?

Homework Statement A pilot wishes to fly at maximum speed due north. The plane can fly at 100km/h in still air. A 30km/h wind blows from the south-east. Calculate: a) The direction the plane must head to fly north. b) Its speed relative to the ground. Homework Equations Sine Rule...

So, velocity is a vector, right? And vectors can't have negative magnitudes, right? Then why is leftward velocity considered negative in 1D kinematics? It just seems off to me. Same with acceleration, and pretty much _every vector in all of physics._

The context for the question is in the attachments (pg1.png, pg2.png, pg3.png), so there is some reading involved. Although, it is a short and simple read if anything. The inquiry is in (inquiry.png). My understanding of the situation is that Q(t) abides by the differential equation Q'(t)Q(t)T...

Let me start off by stating a given problem: A baseball is hit, and leaves the bat at a speed of 100 mph and at an angle of 20° from the horizontal. Express this velocity in vector form. So we're given the velocity and the angle at which the ball is hit. The speed corresponds to the vector's...

Hi, Is there a method to represent a known two-dimensional vector field w of two coordinates x and y with zero divergence and non-zero curl as $$ \vec{w}(x,y) = a \nabla b \, , \hspace{4mm} \nabla \cdot \vec{w} = 0 \, , \hspace{4mm} \nabla \times \vec{w} = f(x,y) \, ?$$ How would one proceed to...

I am trying to understand why an accelerating charge emits radiation/electromagnetic waves but a uniformly moving one does not. I saw one video on Youtube where it seemed that it was explained by the fact that with a uniformly moving charge the Poynting vector was pointing 'in to the volume' -...

Hello, I am having trouble comprehending how grids are made and defined in computers. What is the unit that they use and how is it defined ? I know that softwares use standardized units of measure (measurement) such as centimetre. Basically, how is a 3-Dimensional Space created in computers...

Hello. I'm currently entering into a Physics II class at the start of my third semester at UCONN (my first semester was introductory modern physics - kinetic theory, hard-sphere atoms, electricity and magnetism, scattering, special relativity, Bohr model, etc), and finished Physics I off with...

Hi. I want to normalize a discretized function ##p_{k,k'}##, to satisfy simultaneously two conditions. The normalized function ##p^*_{k,k'}## has to satisfy simultaneously: 1) ##\sum_{k=1}^{M} p^*_{k,k'} w_k=1##, for all ##k'=1,2,...,M##; 2) ##\sum_{k=1}^{M} p^*_{k,k'} w_k \hat \Omega_k \cdot...

Hello PF, I was reading Carroll’s definition of the commutator of two vector fields in “Spacetime and Geometry”, and I’m having (I think) a simple case of notational confusion. He says for two vector fields, ##X## and ##Y##, their commutator can be defined by its action on a scalar function...

Homework Statement For a left invariant vector field γ(t) = exp(tv). For a gauge transformation t -> t(xμ). Intuitively, what happens to the LIVF in the latter case? Is it just displaced to a different point in spacetime or something else? Homework EquationsThe Attempt at a Solution

Homework Statement Homework Equations Is my solution correct? If not then please point out the mistakes and help me solve this question in the right way. Thanks in advance. The Attempt at a Solution

Disclaimer: I am not a physicist, just trying to learn some parts of it in my free time. And I do not mean to propose any kind of "new-theory" with my question. I always thought that Maxwell equations in their differential form for B and E may be reformulated/updated to include a magnetic...

f(\vec{x}+\epsilon \vec{y})-f(\vec{x})=\epsilon \mbox{d}f_{\vec{x}}(\vec{y})+O(\epsilon^2). Is ##\mbox{d}f_{\vec{x}}(\vec{y})## dual vector and why? Is it because ##\mbox{d}## is linear transformation? Also why equality f(\vec{x}+\epsilon \vec{y})-f(\vec{x})=\epsilon...

Hi there I'm having a hard time trying to understand how come ∂r^/∂Φ = Φ^ ,∂Φ/∂Φ = -r^ -> these 2 are properties that lead to general formula. I've been thinking about it and I couldn't explain it. I understand every step of "how to get Divergence of a vector function in Cylindrical...

Suppose I have a vector space V and a matrix M such that multiplying every vector in V by M creates another vector space W. Now suppose I have another matrix A that I can also use to change vectors in V into other vectors. Does there exist a third matrix B such that - for any vector v1 in V -...

Homework Statement Two points in a plane have polar coordinates P1(2.500m, pie/6) and P2(3.800m, 2pie/3) . Determine their Cartesian coordinates and the distance between them in the Cartesian coordinate system. Round the distance to a nearest centimeter.Homework Equations Ax=Acosθ Ay=Asinθ...

I am trying to improve my understanding of Lie groups and the operations of left multiplication and pushforward. I have been looking at these notes: https://math.stackexchange.com/questions/2527648/left-invariant-vector-fields-example...

I know that a vector is a tool to help with quantities that have both a magnitude a direction. At a given point in space, a vector has a particular magnitude and direction and if we take any other direction at the same point we can get a projection of this vector in that direction. Tensor is a...

I know that n-body problem can be complicated, but that's for the dynamics. What about a static case: e.g. if I have the distances of several bodies A, B and C etc. and their distance to a reference mass m, can I just use the vector addition of the Newton's gravitational force to add up all of...

Homework Statement Let a charge oscillate on a straight line between -a to +a with a frequency ω and according to the law: κ (x.t) = κ° sin(πx/a) e^(-iωt) I have to find the following: 1. Vector potential in the dipole approximation 2. Integral of the intensity of radiation Homework...

In Special Relativity, we have the four vector, (E/c, px, py, pz). However, isn't the first term just `p` given that `E=pc` for a photon? Why is it an energy-momentum four vector when the first term isn't really energy but momentum?

I just ran into a Scientific American article (link below) based on a recently updated paper (2nd link). https://www.scientificamerican.com/article/quantum-physics-may-be-even-spookier-than-you-think/ https://arxiv.org/abs/1707.09483 It was the first time I had run into the term "Two-State...

ei=i+j+2vk , how to find the dual basis vector if the above is a natural base?

Homework Statement >There are three vector $$ \vec a ,\vec b, \vec c$$ in three-dimensional real vector space, and the inner product between them $$\vec a . \vec a=\vec b.\vec b=\vec a.\vec c=1, \vec a.\vec b=0, \vec c.\vec c=4 $$ When setting $$x = \vec b.\vec c$$ , (dot here means dot...

|r|2=r.r=uiei.ujej Why are i and j different because we are dotting the same vector?

Homework Statement Let V = RR be the vector space of the pointwise functions from R to R. Determine whether or not the following subsets W contained in V are subspaces of V. Homework Equations W = {f ∈ V : f(1) = 1} W = {f ∈ V: f(1) = 0} W = {f ∈ V : ∃f ''(0)} W = {f ∈ V: ∃f ''(x) ∀x ∈ R} The...

Griffith's writes in chapter 7 electrodynamics that D1.a - D2.a = sigma. a. But minus sine comes when we evaluate the dot product first. How does the minus sign occur without evaluating the dot product?

If we have a some wire (length L) with a PD of V from one end to the next and a current I moving along it we can work out the Poynting vector. It's pointing radially inwards and so tells you the energy per unit time per unit area flowing into the the surface of the wire. What I don't understand...

I have seen the other threads on an infinitely long wires vector potential.Its obvious that really small wires are just infinitely long cylinders: ∇xA=B ∫∇xA.da=∫B.da ∫A.dl = ∫B.da = φ(flux) For an infinite cylinder A.2πri=B.2πrih A=Bh A=μ0*I*h/(2π*r) Now for a cylinder of radius limr->0 =>...

Hi guys, I have encountered a problem in fluid mechanics that gives a three-dimensional vector differential equation \begin{equation} a \vec{f} + \nabla{a} + b \nabla{c} = \vec{0} \end{equation} where a, b, and c are unknown scalar functions of three-dimensional space and f is a known vector...

Homework Statement I don't understand how to form an equation using the knowledge that, 'When ##t=4##, ##P## is moving parallel to the vector ##\mathbf {j}##'. I've seen the solution, and not a single part of it makes sense. I haven't attempted any question like this before, so I have no idea...