Scalar Definition and 829 Threads

Homework Statement If the magnitude of the sum of two vectors is less than the magnitude of either vector, then: -the vectors must be parallel and in the same direction -the scalar product of the vectors must be negative -none of these -the scalar product of the vectors must be...

u and v are contained in V Lets say the scalar multiplication is defined as: ex. ku=k^2 u or ku = (0,ku2) u=(u1,u2) does this mean that this is also the same for different scalar m? mu=m^2 u or mu = (0,mu2) u=(u1,u2) and does this mean the same for any vector v kv=k^2 v or...

u and v are contained in V Lets say the scalar multiplication is defined as: ex. ku=k^2 u or ku = (0,ku2) u=(u1,u2) does this mean that this is also the same for different scalar m? mu=m^2 u or mu = (0,mu2) u=(u1,u2) and does this mean the same for any...

Homework Statement Express the 5.2-kN force F as a vector in terms of the unit vectors i, j, and k. Determine the scalar projections of F onto the x-axis and onto the line OA. I have attached an image of the problem. Homework Equations Fx = Fcos(θ) Fy = Fcos(θ) Fz = Fcos(θ)...

Brian Powell [bapowell] has a new paper out - Scalar runnings and a test of slow roll from CMB distortions, http://arxiv.org/abs/1209.2024. This is interesting and challenges some of the more radical ideas that are currently popular. Very nice, Brian!

Identify each of the quantities below as Vector or Scalar. Speed of a train. (Vector) Volume of a cube. (Scalar) Acceleration of a rocket. (Vector) Mass of a pint of milk. (Scalar) Velocity of a train. (Vector) Force of gravity. (Scalar) I put my answers in parentheses but I am not...

Hello! I am preparing for an exam, I didn't really had much time for, and it would be nice of you if you could help me! Homework Statement Draw a figure, so that the following is true: (AC - AB) * AB = 0 2. The attempt at a solution Since I had to miss some classes, I don't really have...

Homework Statement In the problem, the electric scalar and vector potentials are, \phi=0, \vec{A}=A_0 e^{i(k_1 x-2k_2y-wt)}\vec{u_y} I have to find E, B and S. Then, I have to calculate \phi ' that satisfies div\vec{A}+\frac{\partial \phi '}{\partial t}=0 Then calculate E and B...

Can anyone clarify the concepts of zero vector and zero scalar? -Devanand T

I have the vector: {\bf{u}}(x,y) = \frac{{x{\bf{i}} + y{\bf{j}}}}{{{x^2} + {y^2}}} Where: x = a\cos t y = a\sin t I know I need to use the equation \int\limits_0^{2\pi } {{\bf{u}} \cdot d{\bf{r}}} And the answer is \int\limits_0^{2\pi } {} ((a\cos t/{a^2})( - a\sin t) +...

In this expression the junk on the left is a scalar. The stuff before the integral is another scalar. The integral is a time-like curve between x1 and x2 and at imagine fgf(x1) is a lower left corner of the rectangle and fgf(x2) is the upper right corner and x2-x1 is the length of the base of...

Homework Statement Find vector and scalar equations that passes through point P(3,7,-1) and is perpindicular to the line of intersection of 2 planes. P1:x-y-2z+3=0 P2: 3x-2y+z+5=0 So initially i started by finding the line between the two planes. N1 Does Not Equal N2 so they are not...

Which is the mass dimension of a scalar filed in 2 dimensions? In 4 dim I know that a scalar field has mass dimension 1, by imposing that the action has dim 0: S=\int d^4 x \partial_{\mu} A \partial^{\mu} A where \left[S\right]=0 \left[d^4 x \right] =-4 \left[ \partial_{\mu} \right]=1...

It's impossible that the higgs boson was the only scalar boson in nature. Could quantum-nonlocality be mediated by scalar boson or connected with scalar field? How do you discount or refute this?

Homework Statement I have the following task: In quantum free scalar field theory find commutators of creation and anihilation operators with total four-momentum operator, starting with commutators for fields and canonical momenta. Show that vacuum energy is zero. Homework Equations...

I'm having trouble fully understanding what electrical potential means. If there are two point charges of opposite signs and a point charge somewhere around them, we simply add the two voltages separately? Not as a vector sum? Also the concept of negative potential, does this mean that the...

So, in the calculation of D(t,r) = \left[ \phi(x) , \phi(y) \right] , where t= x^0 - y^0,~ \vec{r} = \vec{x} - \vec{y} you need to calculate the following integral D(t,r) = \frac{1}{2\pi^2 r} \int\limits_0^\infty dp \frac{ p \sin(p r) \sin \left[(p^2 + m^2)^{1/2} t \right]} { (p^2 + m^2...

Homework Statement We have a matrix Anxn (different than the identity matrix I) and a scalar λ=1. We want to check if λ is an eigenvalue of A. Homework Equations As we know, in order for λ to be an eigenvalue of A, there has to be a non-zero vector v, such that Av=λv The Attempt at a Solution...

I am trying to create (in matlab) an irradiance distribution in a 2-D array, using the exact scalar method. As of now I have a 2-D array defined as my aperture function and I also have a 2-D array defined as a Gaussian function (light source). I believe that I know how to do this with a...

Homework Statement Find the Scalar Equation of a Plane containing the points P(1,1,-1) Q(0,1,1) Homework Equations ax + by+ cz = d The Attempt at a Solution PQ = [-1,0,2]T [x,y,z]T = [1,1,-1] + s[-1,0,2]T + t[a,b,c]T ^ This is the vector equation.

If you Lorentz transform a scalar: U^{-1}(\Lambda)\phi(x)U(\Lambda)=\phi(\Lambda^{-1}x) If you now perform another Lorentz transform, would it it look like this: U^{-1}(\Lambda')U^{-1}(\Lambda)\phi(x)U(\Lambda)U(\Lambda')=\phi(\Lambda'^{-1}\Lambda^{-1}x) ? But isn't this wrong...

Need to find the Ricci scalar curvature of this metric: ds2 = e2a(z)(dx2 + dy2) + dz2 − e2b(z)dt2I tried to find the solution, but failed to pass the calculation of Riemann curvature tensor: <The Christoffel connection> Here a'(z) denotes the first derivative of a(z) respect to z...

Homework Statement Need to find the Ricci scalar curvature of this metric: ds2 = e2a(z)(dx2 + dy2) + dz2 − e2b(z)dt2 Homework Equations The Attempt at a Solution I tried to find the solution, but failed to pass the calculation of Riemann curvature tensor: <The Christoffel...

the potential difference between b and a is defined as follows: V(b) - V(a) = -∫E \bulletdl the integral is taken from a to b. so the potential of a positive charge, with infinity as reference, is V(r) - V(infinity) = V(r) = -∫E \bulletdl the integral is from infinity to r...

I'm trying to prove the conformal invariance (under g_{\mu\nu}\to\omega^2 g_{\mu\nu}) of \bar{\Box}{\bar{\phi}}+\frac{1}{4}\frac{n-2}{n-1}\bar{R}\bar{\phi} I've found that this equation is invariant upto a quantity proportional to...

In Physics it seems quantities are either Scalars or Vectors (let's not get into tensors, but if there are other types, please tell me). Vectors I understand reasonably well. Scalars, however, I'm not so sure about: Consider the Scalar quantity of Temperature. There is absolute zero, but...

In the Einstein tensor equation for general relativity, why are there two terms for curvature: specifically the curvature tensor and the curvature scalar multiplied by the metric tensor?

Hi, I'm trying to find a general expression for the scalar triple product for 3 vectors in a simultaneous configuration, that depends only on the inter-vector angles, A1, A2 and A3. I have expressed this quantity in terms of the spherical polar coordinates of the vectors (the length being...

Homework Statement Find the vector x and the scalar λ which satisfy the equations x \wedge b = b-λc,\; x.c=-2where b = (-2, 1, -1) and c = (1, -2, 2) Homework Equations Vector algebra.The Attempt at a Solution First, i worked on x.c=-2 Let vector x = (x_1, x_2, x_3) So, i got the first...

-3i-j+5k = t (root34/102 (11i-13j+4k))-s(-j-k)+r(2i+2j+k) how do i write this eqn as 3 scalar equations and a system of three linear eqns for the three parameters r,s, and t. PLEASE HELP...

Homework Statement I understand the premise of Noether's theorem, and I've read over it in as many online lectures as I can find as well as in An Introduction to Quantum Field Theory; Peskin, Schroeder but I can't seem to figure out how to actually calculate it. I feel like I'm missing a...

We know that work is the dot product between force and displacement .. so dot product always gives scalar (horizontal projection etc) hence work is a scalar quantity? I want the reason behind it... we always do work in specific direction.. suppose a man in appliying force at the angle...

Homework Statement In Wald's text on General Relativity he makes an assertion that I'm not sure why it is allowed mathematically. Here's the basic setup: Let \omega_{b} be a dual vector, \nabla_{b} and \tilde{\nabla}_{b} be two covariant derivatives and f\in\mathscr{F}. Then we may let...

A scalar like electric potential. Say I have a positive charge, and 4m to the right, and 3m up is a point P. If I wanted to calculate the potential at point P, I'd use V=kQ/r (r=√(4^2 + 3^2)). But I'm confused about why finding the potential at 4m to the right (the x component), and the...

Homework Statement Determine the value of k so that the line with parametric equations x = 2 + 3t, y = -2 + 5t, z = k is parallel to the plane with equation 4x + 3y – 3z -12 = 0. Homework Equations The Attempt at a Solution let k=a + bt x=2+3t y=-2+5t z=a+bt direction...

Homework Statement r=xi+yj+zk and r =\sqrt{x^2 + y^2 + z^2} Let f(r) be a C2 scalar function Prove that \nablaf = \frac{1}{2}\frac{df}{dr}r Homework Equations Vector identities? The Attempt at a Solution \nablaf = (\frac{df}{dx} , \frac{df}{dy} , \frac{df}{dz})...

My question is at the bottom of this post PREAMBLE: If a dipole is turned by an angle θ (in a uniform electric field) then the torque applied on the dipole by the electric field will be: τ = 2.q.a.E.sin(-θ) = -2.q.a.E.sin(θ) with the negative sign referring to it being a "restoring" torque...

Homework Statement Let vectorB= 5.45 m at 60°. Let C have the same magnitude as A and a direction angle greater than that of A by 25°. Let B·A = 32.4 m2 and B·C = 35.1 m2. Find the magnitude and direction of A . Homework Equations A·B=MagAxMagBcosθ The Attempt at a Solution I just...

Homework Statement I have a function F defined in a slightly strange way, and I'm not asked to test if curl(F) == 0, but I thought I would do this as part of my working out. Lo and behold, it looks like it doesn't == 0, and this means, as far as I know, that there is no scalar potential but...

Homework Statement Find the scalar equation of the plane containing the points A(-3, 1, 1) and B(-4, 0, 3) and the vector u = [1, 2, 3]. Homework Equations I am at a lost, since I can't tell how to figure out the normal vector. I am supposed to find: Ax+By+Cz+D=0, where [A,B,C] is the...

What's the algorithm for finding scalar function satisfying div f=F if I know vector F?

We all know that for the gravitational field we can write the Poisson Equation: \nabla^2\phi=-4\pi G\rho But I was wondering if, mathematically, we can write the same equation for a scalar field which scale as r^{-2}. Here is the thing. When you deal with gravity, the Poisson equation is...

What is a "scalar (under rotation) 1-chain"? Hi all, I am trying to make sense of a paper involving differenital geometry and Lie algebras. Here's the part I am confused about: Now things begin with finding the cohomology of a Lie algebra. The galilean algebra is taken as an example, and...

How to prove that \nabla x (\phi\nabla\phi) = 0? (\phi is a differentiable scalar field) I'm a bit confused by this "differentiable scalar field" thing...

Okay this might be a nooby question, but it bothers me. What is the difference between the line integral of a scalar field and just a regular integral over the scalar field? For a function of one variable i certainly can't see the difference. But then I thought they might be identical in...

Special relativity predicts that electric fields transform into magnetic fields via Lorentz transformations and that the vice versa also occurs. It also has been argued, since experiments verifying the quantum mechanical phenomenon of the Aharonov–Bohm effect, that the vector potentials are more...

Homework Statement Prove: If a matrix A commutes with all matrices B \in M_{nxn}(F), then A must be scalar - i.e., A=diag.(λ,...,λ), for some λ \in F. Homework Equations If two nxn matrices A and B commute, then AB=BA. The Attempt at a Solution I understand that if A is scalar, it...

Homework Statement A x (B dot C) (A x B) dot C They are vectors. Homework Equations A x (B dot C) (A x B) dot C The Attempt at a Solution I know how to do my homework, but I am confused on these formulas. Is the first formula "A x (B dot C)" the same as the second one? I know the...

Homework Statement Look up, figure out, or make an intelligent guess at the product rule for the scalar product. That is, a rule of the form d/dt [a(t).b(t)] =?+? Verify your proposed rule on the functions a(t) = ti + sin(t)j + e^(t)k and b(t) = cos(t)i - t^(2)j - e^(t)k: Homework...

Homework Statement Consider the scalar field V = r^n , n ≠ 0 expressed in spherical coordinates. Find it's gradient \nabla V in a.) cartesian coordinates b.) spherical coordinates Homework Equations cartesian version: \nabla V = \frac{\partial V}{\partial x}\hat{x} +...