Cross Definition and 1000 Threads

If I choose the positive y direction to be vertically downwards, and the positive x direction to be to the right, and take the cross product y cross x, then the direction of the resultant is out of the page (if I draw x and y as lines on paper). The magnitude is yx sin(φ), where φ is the angle...

Homework Statement This is a general question about the equation. So, I know that the cross product requires a vector in at least 3 dimensions crossed with another. Here is the formula that I am using: uxv = My problem is the negative/positive sign orientation in front of the y element and z...

The electrons flow on the outer surface of the resistor, why then does the resistance of a resistor depend on it's cross sectional area and not on it's perimeter?

Homework Statement I'm finding conflicting statements. One says that current is measured as the amount of charge per time that enters through a cross sectional area. Another says that current is measured as the amount of charge per time that passed through a point. Could someone clarify this...

Hi - just working through my text (studying by correspondence) on Del operator - so Curl, div etc. Came across some identities parts of which which have me confused. what does it mean when a vector is shown as multiplying something - but without dot or cross? For example F(∇.G) or ∇(F.G) or...

1. Situation: I have no specific exercise in mind but just the general form. ''A beam of protons is colliding with a plate of a given particle density ##\rho## and thickness ##l##. The cross section is ##\sigma##. What should the thickness of the plate be such that the intensity of the outgoing...

I guess the title really says it all. I'm reading "space-time algebra" by David Hestenes, and he explains the properties of the wedge product (area of parallelogram, antisymmetric, etc.) and it sounds just like the cross product to me. He then says clearly however that this is not to be...

When we talk about the angle between two vectors while computing the cross product, which angle are we referring to exactly? According to most sources, the angle should be between 0 and π; yet according to my math book, "the angle is measured in an anticlockwise sense from a to b, if the vector...

Hello, I'm having some difficulty with a conceptual question on a practice test I was using to study. I have the answer but not the solution unfortunately. 1. Homework Statement "For every differentiable function f = f(x,y,z) and differentiable 3-dimensional vector field F=F(x,y,z), the...

Greetings, i need the absorption cross section for the absorption of an H-alpha photon by a hydrogen atom, in the correct state of course, which I'm pretty sure is neutral hydrogen, n=2. I am needing this for a project, so i also need a reliable source where this comes from. Thanks beforehand...

Homework Statement I could prove a, trying b now. Homework Equations The definition of the cross prod.? The Attempt at a Solution https://www.dropbox.com/s/0sauaexkl4j2yko/proof_cross_prod.pdf?dl=0 I did not manage to get a scalar times v and a scalar times w. (No need to point this...

Homework Statement Given that \vec{V} and \vec{W} are vector operators, show that \vec{V}\times \vec{W} is also a vector operator. 2. The attempt at a solution The only way I know how to do this is by showing that the commutator with the angular momentum vector operator ( \vec{J}) is zero...

I tried another approach to the problem of covariance like in Bell's theorem :from the definition ##Cov(A,B)=\langle\Psi|A\otimes B|\Psi\rangle-\langle\Psi|A\otimes 1|\Psi\rangle\langle\Psi|1\otimes B|\Psi\rangle## (##A=diag(1,-1)=B##) we can see that this 'average' is in fact a quadratic form...

Homework Statement Find vector product of C = A \times B of two vectors in oblique coord. system. Give explicit expressions of components of C in covariant and contravariant components (constructing reciprocal basis from direct basis will be useful). Homework Equations I am basically just...

I am looking for a realistic explanation of the double-slit experiment in terms of wave packets (instead of stationary waves). First of all this results in using the scattering cross section, i.e. the probability current (not the density). Then, I guess, there is a kind of time average. So one...

I'm looking to buy a semiconductor cross reference book, for part numbers and diode and transistor parameters, including new smt parts. I had an old sgs Thomson book but it got lost in a move, if anyone could recommend me one that would be great. I don't want a link to a website cross...

This isn't a homework problem. I am preparing for a particle physics exam and although I understand the theoretical side of field theory, I have little idea how to approach practical scattering questions like these. THE PROBLEM: Dark matter might be observed at the LHC with monojet and...

We have a solid cube with some mass that we fire as a projectile at some angle. The cube is launched in such a way that two of the faces are perpendicular to the initial velocity vector. Assuming there is air resistance, would the cube change its orientation while it flies, even if the mass is...

Homework Statement If the electric motor of problem 3.66 is to be mounted at the free end of a steel cantilever beam of length ##5## m and the amplitude of vibration is to be limited to ##0.5## cm, find the necessary cross-sectional dimension of the beam. Include the weight of the beam in the...

Homework Statement An object is rotating at 4 rad/s about an axis in direction of (2 \hat{i} - 4 \hat{j} + 3\hat{k} ) which then passes through a point (1,2,0)m . Calculate the instantaneous velocity at the point (2,0,3)m (Hint: use \vec{v} = \vec{\omega} \times \vec{r} )Homework Equations...

From my understanding, average trajectories based on weak "measurements", obey the 'no-crossing rule'. These average trajectories strongly resemble the single-photon trajectories predicted by Bohmian mechanics: For instance compare these average trajectories...

Homework Statement Considera 1.0 C charge moving with a velocity of v = -2.0i + 2.0j - 1.0k in a magnetic field of B = -4.0i + 1.0j – 3.0k. What force is this charge experiencing? What is the angle between the velocity and magnetic field vectors? Homework Equations F = q(E + v x B)...

Hi, I was provided a http://eng-tips.com/viewthread.cfm?qid=372664# that I'm lost on. I was given an equation that we solved for earlier in the semester using the finite difference (dx method). (first image below). The http://eng-tips.com/viewthread.cfm?qid=372664# wasn't clear when...

Homework Statement Use the LC symbol to calculate the following: $$\nabla \times \frac{\vec{m} \times \hat{r}}{r^2}$$ Where ##\vec{m}## is just a vector, and ##\hat{r}## is the unit radial vector and ##r## is the length of the radial vector. Homework Equations On the Levi Civita symbol...

Is this just a coincidence that cross product can be found from determinant of 3*3 matrix? what is the differences between wedge product and cross product?Thanks.

A fluid motion has velocity $$\underline{u}=\sin{(at)}\hat{\imath}+\hat{\jmath} \times r +\cos{(at)}\hat{k}$$ I need to know what is $$\hat{\jmath} \times r$$ to find Vorticity and other things.

Is A x B = | i j k | also true for Spherical Coordinates? | r1 theta1 phi1 | | r2 theta2 phi2 | Or I have to convert them to Cartesian Coordinates and do the cross product and then...

Is there an intuitive reason or proof demonstrating that in general dimensions, there is no direct analogue of the binary cross product that yields specifically a vector? I came across Wedge Product as the only alternative, but am just learning linear algebra and don't quite comprehend yet...

HEY GUYS! (Wave) ok so i have this question i did. and now I am reviewing for the test and i looked at how i did it and i did in the most complicated way ever. i don't FULLY understand chegg's method. so i hope someone can provide me with the SIMPLEST method possible. thank u! (Blush) (p.s...

Homework Statement A and B are two unit vectors in the x-y plane. A = <cos(a), sin(a)> B = <cos(b), sin(b)> I need to derive the trig identity: sin(a-b) = sin(a) cos(b) - sin(b) cos (a) I'm told to do it using the properties of the cross product A x B Homework Equations A x B =...

Homework Statement Vectors A & B lie in an xy plane. A has a magnitude 7.4 and an angle 142(deg) with respect to the +x direction. B has components (-6.84i, -7.37j) B) What is the angle between the -y axis and the direction of the Cross product between A and B? Homework Equations Cross...

Hi. Is using the Levi-Civita symbol to calculate cross-product combos like A x (B x C) allot faster than just using the good old determinant method? I ask because my lecturer in electrodynamics 2 told us it is better, but it seems to me that it's going to cost me time to learn to use this...

Why are absorption cross sections for atoms so much larger than that of molecules. For example, the absorption cross section for the D2 line in Rubidium is ~1E-9 cm^2. Specifically, the cross section is basically σ~λ^2 The absorption cross sections for say, I2, is 9 orders of magnitude...

Homework Statement What is the cross section if the density of atoms in a material is 10^26 metres-3, and 0.04% of a beam of neutrons is stopped in a 2 cm slab of the material ? Homework Equations Sigma = event rate per nuclei / incident flux The Attempt at a Solution I have...

Given a monoenergetic beam of photons, how are the interaction cross sections used to calculate a) the dose rate to a small volume of tissue, and b) the exposure rate. I assume this question references the below equations: \dot{D} = \theta ( \frac{μ}{ρ} )_{med} * E_{ab} \dot{X}...

Hi there. I wanted to demonstrate this identity which I found in a book of continuum mechanics: ##curl \left ( \vec u \times \vec v \right )=div \left ( \vec u \otimes \vec v - \vec v \otimes \vec u \right ) ## I've tried by writting both sides on components, but I don't get the same, I'm...

I have a question regarding the calculation of the cross section in muon pair production from electron positron annihilation. After some calculations the textbook comes to the conclusion that the differential cross section is approximately equal to: (1+cos(theta)^2)alpha^2/(4*s) where alpha...

[SIZE="4"]Definition/Summary The cross product of two vectors \mathbf{A} and \mathbf{B} is a third vector (strictly, a pseudovector or axial vector) \mathbf{A}\times\mathbf{B} perpendicular to both of the original vectors, with magnitude equal to the product of their magnitudes times the...

Homework Statement The question asks for resistance R of a disk with radius r and fixed width w, whose cross sectional area is variable. Unlike in the picture below, the resistor is not connected to the circuit on the flat ends, but on the cylindrical sides. Homework Equations...

I understand that dot product of vectors means projecting one vector on to the other. But I don't understand what is the physical significance of a cross product? I have read that cross product gives the area of the parallelogram which has each of the vectors as its sides...but why do we want to...

How do I calculate radar cross section given the diameter of a spherical object and the radar's frequency in GHz? Thanks

hello, i need the values for the absorption cross sections of positive hydrogen ions for a specific set of wavelengths, Halpha to start with. At first i thought finding this on the web was easy, but turns out to not be trivial at all. If you can help me, i also need the (reliable) source...

Hi everyone, I have to find out how to do cross and dot product for two vectors in non-orthogonal coordinate system. thanks

I was looking into what cylinders need pairing to make a set 0f 180 headers for an LS V8 engine. When looking the pairings shown below. LS firing order 1-8-7-2-6-5-4-3 Passenger (L) side = 1 3 5 7. Driver side (R) 2 4 6 8 1-8-7-2-6-5-4-3 L-R-L-R-R-L-R-L for a 4-1 header I get. 1-7-6-4...

1. Here is the prompt: http://imgur.com/mfbPidG 2. F = qv x B 3. At first this seemed like a simple cross product problem, and it probably still is, but I'm really confused as to what "3.70E6 m/s/ in the (i+j+k)/sqrt(3) direction" means, so I don't know how to set up my problem anymore. Could...

I'm trying to find specific reaction cross section 18O(p,n)18F in proton + O-18 TENDL (ENDF format). # p + 18O : (p,n) Total # Q-value =-2.51902E+00 # E-threshold= 3.64964E+00 # # energies = 45 # E xs 1.000E+00 0.00000E+00...

Here is the claim I am trying to prove: Suppose we have two vectors \mathbf{r} and \mathbf{s}. I would like to show that there are only two directions in which the resultant vector of the cross product \mathbf{r} \times \mathbf{s} can point, parallel and antiparallel. How might one prove...

A long piece of sheet metal w inches wide is to be bent into a SYMMETRIC form with three straight sides to make a rain gutter. A cross section is shown below. \_____/ The base is w-2x and the angled side lengths are both x with a theta between top horizontal. A. Determine dimensions that...

The base of a solid is the region bounded by the parabola $$y^2=4x$$, and the line $$x=2$$ . Each plane section perpendicular to the x-axis is square. (I assume this means the cross-section of the solid will be square) then we are not revolving but slicing. The volume of the solid is? (the...

1."In this exercise, you will be finding the resultant torque from the cross product of a lever arm with a force vector. The lever arm vector is A=2.0i+3.0j. The force vector is B=3.0i-4.0j. Find A x B B x A and 2A x 3B 2.My teacher has been sick the past few days so hasnt taught us...