Vector Definition and 1000 Threads

[ Moderator note- Edited to re-insert formatting template headers] Hi guys, I am stuck at this problem, Homework Statement Here it is given that an insulating sphere of radius a, carries a charge density ρ=ρ'( a^2-r^2)cosθ, when r <a. How will the leading order term for the electric field at...

Hi, hopefully a quick question here...how do you calculate the angle between two vectors if the only information you have is the value of their scalar product and the magnitude of their cross product? Thanks! Andy

I've been racking my brain for a while now over what I feel should be a simple problem to solve, but my answer is wrong. I'm not wildly wrong, but wrong enough to think I've made a proper error and it's not just a rounding error or something. The question goes like this: A dog in an open field...

hello every one can one please construct for me left invariant vector field of so(3) rotational algebra using Euler angles ( coordinates ) by using the push-forward of left invariant vector field ? iv'e been searching for a method for over a month , but i did not find any well defined method...

Homework Statement The problem statement is simply to find the vector potential inside and outside an infinite wire of radius R, current I and constant current density j using the Poisson equation. Homework Equations The Poisson law can be written A = μ0 /4π *∫(I/r*dl) or A = μ0 /4π *∫(i/r*dV)...

To me the state vector represents the following... 1) The number of elements in the state vector is the number of possible outcomes. Call that number n. 2) The value of each element in the state vector is the probability amplitude associated with that outcome. If that is true, then it seems to...

Homework Statement A bullet was shot at 40m/s Elevation angle : 37° Bullet mass = 0.01 Kg Question : how much work is done by the force of gravity to the bullet since it was shot until it reaches the ground again Homework Equations mgh = E.Pot 1/2mv ^2 = E kinetic The Attempt at a Solution...

Hello, I have a question about why I can't determine the angle between two vectors using their cross product. Say there are two vectors in the XY-plane that we want to find the angle between: A = -2.00i + 6.00j B = 2.00i - 3.00j The method to do this would be to work out the scalar product of...

Homework Statement [/B] Let f and g be scalar functions of position. Show that: \nabla f \cdot \nabla(\nabla ^2 g)-\nabla g \cdot \nabla(\nabla ^2f) Can be written as the divergence of some vector function given in terms of f and g. Homework Equations [/B] All the identities given at...

Let $a, b \in \Bbb R$ and $u, v \in \Bbb R^2$, with $u = (0, 1)$ and $v = (1, 0)$. Show that every vector in $\Bbb R^2$ is of the form $au + bv$. Under what conditions is this true for general vectors $u = (u_1, u_2)$ and $v = (v_1, v_2)$? No idea where to begin. Would appreciate any help.

Homework Statement Homework Equations RAO = b(Sinβj+Cosβk) The Attempt at a Solution [/B] The box in red is ω. However I am unsure of where they got the box in blue from? As mentioned above, RAO = b(Sinβj+Cosβk) so not sure where they got the box in blue from? I know of the vector triple...

There are two charges with charge q and mass m and they are in equilibrium. Then, in the diagram why is my teacher saying that electrostatic force(F)=mg? Below is diagram.

So, most Relativity textbooks (although some famous, like Weinberg's don't) show us that a vector ##V## is properly written as $$V^\mu(x) \frac{\partial}{\partial x^\mu}$$ where ##V^\mu(x)## are its components at the point ##x## and the "base" in which the vector is written in is the operator...

How do a cut a vector in R? Say I want to split a vector to two parts. One for everything less than 150 and other for everything greater than 150. I tried the cut function but it seems confusing.

Homework Statement Neutral vector mesons with ##J^{PC} = 1^{−−}## include the ##\phi## (mφ = 1020 MeV), ##J/\psi## (mJ/ψ = 3100 MeV), and ##\Upsilon## (mΥ = 9460 MeV), with quark content ss¯, cc¯, and b ¯b respectively. The decays of these mesons go largely to hadronic final states (jets)...

I have recently finished an extensive review of vector calculus. I need to connect the exhaustive techniques of Surface Integrals and line integrals to quite a few problems involving Maxwell's Equations before I really feel certain that I am on board with both the math and the physics. I feel...

Let's assume the vector field is NOT a gradient field. Are there any restrictions on what the curl of this vector field can be? If so, how can I determine a given curl of a vector field can NEVER be a particular vector function?

Hello. I would like to check my understanding of how you transform the covariant coordinates of a vector between two bases. I worked a simple example in the attached word document. Let me know what you think.

Homework Statement Famous quarterback Fleet O. Floote is attempting a quarterback draw by running up the middle toward his goal line at 4.6 m/s. A linebacker hits him squarely, and their combined final velocity is 3.8 m/s at an angle of +120.° from the quarterback's original direction. The time...

Why is there a need to find unit vector? If we are given a vector we can always find its direction.

A long horizontal wire carries 22.0A of current due north. What is the net magnetic field 20.0 cm due west of the wire if the Earth's field there points downward, 40 degrees below the horizontal, and has magnitude 5.0 E-5 T? My approach: 1. Drew north to the right and the wire lying flat, with...

Homework Statement [/B] The door is held open by the means of 2 chains. If the tension in AB and CD is Fa = 300 N and Fc = 250 N, respectively, express each of these in Cartesian Vector Form Homework Equations Sin / cos / tan The Attempt at a Solution The angle of FA at B is...

Suppose we have defined a vector ##V## at a point ##x##, so it has components ##V^\mu(x)## at ##x##. Let ##y## be another point, such that ##y^\mu = x^\mu + \epsilon \zeta^\mu(x)##, ##\epsilon## a scalar. Now, since ##x## and ##y## are coordinate points, the vector ##V## should not depend on...

hello every one . can someone please find the left invariant vector fields or the generator of SO(2) using Dr. Frederic P. Schuller method ( push-forward,composition of maps and other stuff) Dr Frederic found the left invariant vector fields of SL(2,C) and then translated them to the identity...

Hi (1/sqrt(4t²+1), 2t/sqrt(4t²+1)) gives a unit tangent to the curve y=x^2 at point (t,t^2). Viewing the vector as velocity, shouldn't I be able to integrate it and get a parameterization for y=x^2?

Homework Statement The question is: if vectors v1, v2, v3 belong to a vector space V does it follow that: span (v1, v2, v3) = V span (v1, v2, v3) is a subset of V.[/B] 2. The attempt at a solution: If I understand it correctly the answer to both questions is yes. The first: the linear...

Hey guys, I'm new to the forum and I have a question that has stumped several of the professors at my school. My idea is to use an electric motor with a solid rocket engine on a thrust stand to spin the exit cone. The concept would make use of centripetal force to increase the pressure of...

Homework Statement The surfaces ##x^2+y^2 = 2## and ##y=z## intersect in a curve ##C##. Find a unit tangent vector to the curve ##C## at the point ##(1,1,1)##. Homework EquationsThe Attempt at a Solution So I'm thinking that we can parametrize the surfaces to get a vector for the curve ##C##...

Homework Statement Let a is a complex vector given by a = 2π K - i ρ / α^2 , where ρ is a two dimensional position vector and K is the corresponding two dimensional vector in the Fourier space. In order to find magnitude of this vector, i found that it is 4π^2 K^2 + ρ^2 / α^4 . The logic...

Can anybody give me a list of all cross products in physics. I have the following in my list: Torque $$\vec{\tau}=\vec{F}\times\vec{r}$$ Angular momentum $$\vec{L}=\vec{r}\times\vec{p}$$ Velocity $$\vec{v}=\vec{\omega}\times\vec{r}$$ Biot-Savart law $$\vec{dB}=\dfrac{\vec{i...

δij is the Kronecker delta - is this considered a tensor or vector? I know it means the identity when i=j so I'm going to guess tensor because it's a matrix rather than just a vector but I want to make sure. A matrix is a rank 2 tensor and a vector is a rank 1 and a scalar is a rank 0? How does...

Homework Statement F(x,y,z) = xzi Homework Equations N/A The Attempt at a Solution I just said that x = rcos(θ) so F(r,θ,z) = rcos(θ)z. Is this correct? Beaucse I am also asked to find curl of F in Cartesian coordinates and compare to curl of F in cylindrical coordinates. For Curl of F in...

Homework Statement Consider the set V + {all periodic *complex* functions of time t with period 1} Draw two example functions that belong to V. Show that if f(t) and g(t) are members of V then so is f(t) + g(t)Homework EquationsThe Attempt at a Solution f(t) = e(i*w0*t)) g(t) =e(i*w0*t...

Homework Statement Let v(0) = [0.5 0.5 0.5 0.5]T, v(1) = [0.5 0.5 -0.5 -0.5]T, v(2) = [0.5 -0.5 0.5 -0.5]T, and z = [-0.5 0.5 0.5 1.5]T. a) How many v(3) can we find to make {v(0), v(1), v(2), v(3)} a fully orthogonal basis? b) What are z's coefficients of expansion αk in the basis found in...

Homework Statement The texts are taken from http://ingforum.haninge.kth.se/armin/fluid/exer/deriv_navier_stokes.pdf and https://simple.wikipedia.org/wiki/Stress_(mechanics)Homework EquationsThe Attempt at a Solution The formula for stress is ##\sigma=\frac{F}{A}## (I). From the document...

Homework Statement Find the unit vector perpendicular to the level curve of f(x,y) = x2y-10xy-9y2 at (2,-1) Homework Equations Gradient The Attempt at a Solution I'm not sure what it's asking. Wouldn't this just be the gradient of f(x,y) evaluated at (2,-1) then normalized? or am I missing...

Homework Statement Provide a complete proof that a regular plane curve γ : I → R2 can near each point γ(t0) be written as a graph over the tangent line: more precisely, there exists a smooth real valued map x → f(x) for small x with f(0) = 0 so that x → xT(t0) + f(x)JT(t0) parametrizes γ near...

Homework Statement The electric potential at points in an xy plane is given by V = (1.5 V/m2)x2 -(2.9 V/m2)y2. What are (a) the magnitude of the electric field at the point (3.9 m, 2.9 m) and (b) the angle that the field there makes with the positive x direction. Homework EquationsThe Attempt...

Okay so when there is time-translation symmetry because the metric components do not have any time- dependence, ##\partial_x^0## is a Killing vector. I'm just confused what this means explicitly, since a derivative doesn't make sense without acting on anything really? But by 'spotting the...

Hi, I have a question regarding vectors. I am thinking ahead regarding an application that I am writing in OpenGL. Currently, four functions make up the vertex calculations, with one independent variable (w2center, w2normal, w2uv, uv2vector). A per-vertex center variable and per-vertex vector...

Homework Statement Given ## d \vec r = dr \hat r + r d \theta \hat {\theta} + r \sin \theta d \phi \hat {\phi}.## Find ## d \hat r , d \hat {\theta} , d \hat {\phi}. ## Homework Equations I know that ## d \hat {e_j} = \omega^i_j \hat {e_i} ## and that ## \omega_{ij}=- \omega_{ji} ## and ## 0 =...

Is the set of all differentiable functions ƒ:ℝ→ℝ such that ƒ'(0)=0 is a vector space over ℝ? I was given the answer yes by someone who is better at math than me and he tried to explain it to me, but I don't understand. I am having difficulty trying to conceptualize this idea of vector spaces...

Homework Statement 3 charges are placed like shown: Q1 __4cm____ Q2 ______6cm___________Q3 Q1=-2nC Q2= 1nC Q3= 3nC Find the resultant force and its direction upon the charge Q3. Homework Equations F=k0*(Q1Q2)/r2 k0-constant, equals to 9*10^9 r-distance The Attempt at a Solution...

I know that If we have a rigid body rotating clokwise direction,the angular velocity vector should be in the into the screen.But also I know that ##w=dθ/dt## so..Whats the equation that tells us that ##\vec w## is into the screen ? Is it coming from some vector product ? Or we know that...

Homework Statement Find unit vector(s) that are parallel to both of the planes 6x + y + z = 1 and x − y − z = 0 . Homework Equations N/A The Attempt at a Solution OK. So here is my reasoning - I find the normal of both the given planes and find the cross product between the vectors. The...

In a vector space can you limit the scalar. For example, if I have Vector space in ℤ2 can i only multiple integer scalars?

I found it very interesting to see that surface charge and the Poynting vector are being used to describe how a simple DC circuit actually works. Chabay and Sherwood have made an outstanding contribution to physics and engineering in their texts and papers. Of course others jump on the...

Homework Statement How do you find the derivative of the radial vector r Homework Equations r [/B]= ru'_r + ru_r r = \frac{dr}{dt}u_r + r\frac{du_r}{dt} can't get latex to work either The Attempt at a Solution [/B] If r is the magnitude of r, how would you find the derivative of it...

Homework Statement As always, I wish I were allowed to upload a drawing ;) This is not a problem, this is a derivation of sorts, so I don't have any numbers. I have 3 points. one at the origin, a point charge q and a test charge Q I have a vector from the origin to the point charge q with a...

I know that the span of any subset of vectors in a vector space is also a vector space (subspace), but is it true that every vector space has a generating set? That is, the moment that we define a vector space, does there necessarily exist a spanning set consisting of its vectors?