What is Vector: Definition and 1000 Discussions

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...

Hi I wish to use Python to create art which can be exported as dxf files for use with laser cutters.While Processing is available for Python, it only creates raster images. What are my options if I want to create vector images? This may be the wrong forum for this question... If it is, where...

Homework Statement Given $$\phi = x^{2} +y^{2}-z^{2}-1 $$ Calculate the unit normal to level surface φ = 0 at the point r = (0,1,0) Homework Equations $$ \hat{\mathbf n} = \frac{∇\phi}{|\phi|}$$ $$ z = \sqrt{x^{2}+y^{2} -1} $$ $$ \mathbf n = (1,0,(\frac{\partial z}{\partial x})_{P})...

in this problem i can solve v = ω x r = <0, -ωrsinψ, 0> in cartesian coordinates but i don't understand A in sphericle coordinates why? (inside) A = ⅓μ0Rσ(ω x r) = ⅓μ0Rσωrsin(θ) θ^ how to convert coordinate ?

Homework Statement Hello, I am currently studying mathematics and physics on my own, and I ran into a type of problem in physics that is a bit unclear to me. Say we have pulley at the top of an inclined plane with a base angle of alpha and the top angle is alpha. Homework Equations I assume...

Hello! I just started reading about ##Z_2## graded vector spaces (and graded vector spaces in general) and I want to make sure I understand from the beginning. So the definition, as I understand it, is that a graded vector space can be decomposed into subspaces of degree 0 and 1. So ##V=V_1...

Homework Statement I reference problem 9.10 Purcell's Electricity and Magnetism (3rd ed). A very thin straight wire carries current ##I## from infinity radially inward onto a conducting shell with radius R. Show that the total flux of the Poynting vector away from an imaginary tube of radius...

Hi. If I have a vector v , say for velocity for example then v.v = v2 and I differentiate wrt t v.v I get 2v.dv/dt but if I differentiate v2 I get 2v dv/dt but v.dv.dt is not the same as v dv/dt so what am I doing wrong ? Thanks

Reading Chandrasekhar's The mathematical theory of black holes, I reached the point in which the Newman-Penrose GR formalism is explained. Actually I'm able to grasp and understand the usage of null tetrads in GR, but The null tetrads used in this formalism, are very special, since are made by...

Information Given: In the figure, a square of edge length 17.0 cm is formed by four spheres of masses m1 = 4.70 g, m2 = 2.90 g, m3 = 0.800 g, and m4 = 4.70 g. Question: In unit-vector notation, what is the net gravitational force from them on a central sphere with mass m5 = 2.90 g? Attempted...

Homework Statement Homework EquationsThe Attempt at a Solution My answer is d = |(a-b)x(p-b)|/|(b-a|). I first find out the area of the parallelogram produced by BA and BP and divide the area by length AB to get the height. Why am I wrong?

Homework Statement Is the following conclusion correct? Assume there's an equation with vectors on both sides. Taking the dot product of this equation with vectors on both sides loses information, but information will not lose when taking dot products with higher rank tensors on both sides...

I am sure that the vector potential of a toroid isn't 0 even though its magnetic field is , does anyone have a derivation for the its the vector potential at a point P(x,y,z) outside the toroid ? i expect that since its curl is 0 we have a general form of : A = f(!x)ex + g(!y)ey+m(!z)ez Such...

Hi, I've got this problem I'm trying to work out. The problem seems simple, but I don't think I have a good way to construct a way to solve it. This is the problem. Let P and Q be two points with position vectors p and q and let R be a point midway between these two. Find an expression for the...

I studied the vector analysis in Arfken and Weber's textbook : Mathematical Methods for Physicists 5th edition. In this book they give the definition of vectors in N dimensions as the following: The set of ##N## quantities ##V_{j}## is said to be the components of an N-dimensional vector ##V##...

How do we express the locality of a vector space in general relativity? I mean, it's not clear what the boundaries of a given vector space are. To put in another way, we could, in principle, blindly consider that we have the entire of ##\mathbb{R}^4## at our disposal to describe, say, the...

I was going through vector and scalar quantities (the way they are taught in high school), and this is how I think students are supposed to understand it: Scalar quantities are quantities that add like numbers. For e.g. Mass. If I add 100 g of water to a bucket and then add a further 100 g, I...

According to my understanding, option D is the only possible value of R. I don't understand how options A, B and C are included. Please explain this question. Thanks. (regards)

Hi all, i tried to do this question but got stuck on the last point . Can anyone help me please? The general form of vector potential: I got the answer for A1 vector potential but don't know what assumptions i need to get the expression for the A2. Does anyone know how one can derive it...

Homework Statement Problem- Determine if the set of all function y(t) which have period 2pi forms a vector space under operations of function addition and multiplication of a function by a constant. What I know- So I know this involves sin, cos, sec, and csc. Also I know that a vector space...

I feel like the vector space ##\mathbb{R}^n## differs from other vector spaces, like ##\mathbb{P}##. For example, if we wrote down an element of ##\mathbb{P}##, like ##1+2t^2##, this is an object in its own right, with no reference to any coordinate system or basis. However, when I write down an...

I learned that the Poynting vector was the electromagnetic density of momentum but recently, while reading the Electromagnetic_stress–energy_tensor article at Wikipedia, I thought about the implications of the momentum conservation equation and arrived to an inconsistency, this equation is...

Homework Statement Two parallel very long threads are uniformly charged with linear charge density of 10-8 C/cm . Distance between them is 15 cm. Find electric field vector at a distance of 15 cm from both threads. Homework Equations E*dA=Qenclosed/permittivity of free space The Attempt at a...

Homework Statement What's the vector equation for a plane which contains the point ##(-2,2,1)## and whose vectors ##(1,1,2)## and ##(2,1,-1)## are parallel to it? Homework Equations I think the relevant here is - The plane equation. The Attempt at a Solution [/B] We can go through...

AIUI, every normal matrix has a full eigenvector solution, and there is only 1 *normalized* modal matrix as the solution (let's presume unique eigenvalues so as to avoid the degenerate case of shared eigenvalues), and the columns of the modal matrix, which are the (normalized) eigenvectors, are...

Given an ##N## dimensional binary vector ##\mathbf{v}## whose conversion to decimal is equal to ##j##, is there a way to linearly map the vector ##\mathbf{v}## to an ##{2^N}## dimensional binary vector ##\mathbf{e}## whose ##(j+1)##-th element is equal to ##1## (assuming the index starts...

Homework Statement Take as input from the user an integer N. We don't want the user to enter very large integers, so exit with an error message if N>20. You may assume that N is an integer (and not a real number) and also that it is positive. Make two vectors v1 and v2 using v1.append() and...

Homework Statement Write an alternate vector equation for the following line. Change both the point and the direction vector: w⃗ =(4,−1,3)+t(−2,1,7) Homework EquationsThe Attempt at a Solution Did I write a proper alternate vector equation here? I'm still new to vectors in 3-space any tips or...

Homework Statement The velocity of a plane is 625 km/h northwest. a) Draw a diagram of this vector, including the magnitude and direction. b) Determine the horizontal and vertical components of this vector. Round your answers to the nearest whole number. c) Give the coordinates of the vector...

Homework Statement Given the following diagram, use vector addition to sketch the resultants: a) u→−2v→ b) 3v→−u→ Homework EquationsThe Attempt at a Solution For this question I am fairly certain that it is correct but for some reason I'm doubting myself. I was wondering if I could get some...

Homework Statement Find u→ in Cartesian form if u→ is a vector in the first quadrant, ∣u→∣=8 and the direction of u→ is 75° in standard position. Round each of the coordinates to one decimal place. Homework Equations none The Attempt at a Solution I'm certain this is correct, but some guy at...

Homework Statement Hi, I'm having some doubts about the gradient. In my lecture notes the gradient of a scalar field at a point is defined to point in the direction of maximum rate of change and have a magnitude corresponding to the magnitude of that maximum rate of change of the scalar field...

Could we have two vector spaces each with its own set of basis vectors. but these basis vectors are related according to the following way. A particular set of vectors in the first vector space may exist "all over the place" but when you represent the same information in the second vector space...

Hi, let ##\gamma (\lambda, s)## be a family of geodesics, where ##s## is the parameter and ##\lambda## distinguishes between geodesics. Let furthermore ##Z^\nu = \partial_\lambda \gamma^\nu ## be a vector field and ##\nabla_\alpha Z^\mu := \partial_\alpha Z^\mu + \Gamma^\mu_{\:\: \nu \gamma}...

I am confused about tensor invariance as it applies to velocity and energy. My understanding is a tensor is a mathematical quantity that has the same value for all coordinate systems. I also understand that a vector is a first order tensor and energy is a zero order tensor. Thus, they should...

On pg. 60 of Nolting Theoretical Physics 1 for the definition of a vector multiplied by a scalar the book shows two little up arrows if the scalar is greater than zero and an little up arrow and then a little down arrow if the scalar is less than zero. Then again on pg. 61 for definition 1.139...

Given w = |v|∙ u + |u| ∙ v. If θ = ∠(u ∙ w) and φ = ∠(v ∙ w) then …. a. Φ – θ = 90° b. θ + φ= 90° c. θ = φ d. θ – φ = 90° e. θ – φ = 180° What I have done: \cos\theta=\frac{u\cdot w}{|u||w|} and \cos\phi=\frac{v\cdot w}{|v||w|} Then I substituted them as |v| and |u| to the given equation and...

Homework Statement u and v are two vectors in the same plane. Vector OM = u+2v Vector OP = 6u+v Vector OQ = 5u +2v Vector OR =2(VecOM) +v Given that ZPQM is a parallelogram, express Vector OZ in terms of u and v.Homework EquationsThe Attempt at a Solution First they wanted me to find Vectors...

Does it make sense to say that a set together with a field generates a vector space? I came across this question after starting the thread https://www.physicsforums.com/threads/determine-vector-subspace.941424/ To be more specific, suppose we have a set consisting of two elements ##A = \{x^2, x...

Suppose we have a scalar function θ(x,y,z,t) of space and time where theta is some angle (0≤θ≤2π) that represents the compact coordinate of a 3 dimensional space (x,y,z) filling membrane at the space time point (x,y,z,t) in a compact space dimension w. Suppose that charge density "pushes" on the...

Homework Statement Hi I have attached an image which shows OK and OM which are position vectors such that OK=k and OM =m R is the mid point of OK and S is a point on OM such that (vec) OS = 1/3 OM L is the midpoint of RM, using a vector method, prove RS is parallel to KL. Homework...

Homework Statement Determine the vector subspace generated by ##A = \{x^2 -x, 3 - x^2, 1+x \} \subset P^2(x)## Homework EquationsThe Attempt at a Solution I tried the usual check of vector addition and scalar multiplication to get the conditions that ##x## and ##y## should satisfy, but...

Hello Everyone. I am searching for some clarity on this points. Thanks for your help: Based on Schrodinger wave mechanics formulation of quantum mechanics, the states of a system are represented by wavefunctions (normalizable or not) and operators (the observables) by instructions i.e...

Hello, I think I understand what a vector space is. It is inhabited by objects called vectors that satisfy a certain number of properties. The vectors can be functions whose integral is not infinite, converging sequences, etc. The vector space can be finite dimensional or infinite dimensional...

Homework Statement Write a vector equation for the line that passes through the point P(–1, 0, 3) and is parallel to the y-axis. Homework Equations (x,y)=(x_0,y_0)+t(a,b) The Attempt at a Solution u ⃗=(0,1,0) (x,y,z)=(-1,0,3)+t(0,1,0)

Homework Statement Find the scalar, vector, and parametric equations of a plane that has a normal vector n→=(3,−4,6) and passes through the point P(9, 2, –5). Homework Equations Ax+By+Cz+D=0 (x,y,z)=(x0,y0,z0)+s(a1,a2,a3)+t(b1,b2,b3) x=x0+sa1+tb1 y=y0+sa2+tb2 z=z0+sa3+tb3 The Attempt at a...

and Lorentz Gauge. Manipulating Maxwell equations and introducing ##\vec A## vector and ##Φ## scalar potentials the following equations are obtained: ## \nabla^2 \vec A+k^2 \vec A=-μ\vec J+\nabla(\nabla⋅\vec A+jωεμΦ) ~~~~~~~~~~(1)## ## \nabla^2 Φ+k^2 Φ=- \frac ρ ε -jω(\nabla⋅\vec...

Homework Statement Two balls with mass m and 4m collide at the location x=y=0 and stick. Their initial velocities just before the collision can be represented as v1=(i+j) v and v2=(j-i)v' respectively. Their final velocity vf makes an angle θ with the +x axis. Find v and v' in terms of vf and...