Lines Definition and 1000 Threads

We were looking at the spectral lines of sodium in class and I was wondering, why do we see lines, and not any other shape like circles?

Let $$A(2,-1,1)$$, $$B$$ and $$C$$ be the vertices of a triangle where $$\overrightarrow{AB}$$ is parallel to $$\vec{v}=(2,0,-1), $$$$\overrightarrow{BC}$$ is parallel to $$\vec{w}=(1,-1,1)$$ and $$\angle(BAC)=90°$$. Find the equation of the line through $$\(A\)$$ and $$\(C\)$$ in vector and...

Let u=<5,-2,3> and v=<-2,1,4>. Find the value of c which will force the vector w=<2c,3,c-1> to lie in the plane of u and v. I did the cross product of u and v, then i crossed u and w, then I equal the product of u and v with what I got for w. But for some reason when I try doing the triple...

The picture has the problem and my attempts, I need guidance. Thanks in advance

determine whether the lines $L_1$ and $L_2$ are parallel, skew, or intersecting. if they intersect, find the point of intersection. $L_1: \frac{x-2}{1}= \frac{y-3}{-2}= \frac{z-1}{-3}$ $L_2: \frac{x-3}{1}= \frac{y+4}{3}= \frac{y+4}{3}= \frac{x-2}{-7}$ i understand if one vector is the scalar...

find the parametric equations of the line that passes through the points (0,1/2,1) and (2,1,-3) $v= \left\langle 2-0, 1-1/2, -3-1 \right\rangle = \left\langle 2, 1/2, -4 \right\rangle$ $P_0 (2,1,-3)$ $x=2+2t$ $y=1+\frac{1}{2}t$ $z=-3-4t$so my question is, why are the points (2,1,3) used and...

Hi I have a new formula (or at least I think it's new) for predicting the wavelengths/frequencies of hydrogen's spectral lines. Please take a look and tell me if it is new. I am quite confident that it works because Bohr's original formula 'falls out' if one approximates cos(x) as 1 + x^2/2...

Hi PF, please could someone help explain how the bandwidth of a telephone line works. I have read that fibre optics uses light which has a high frequency and therefore can offer a high bandwidth versus a standard telephone line. But what I don't understand is the bandwidth of a standard...

Hey guys i had a question in my paper why electrostatic field lines cannot be discontinuous in charge free region i guessed a weird (but an innovative proof) Tell me is it correct So here it goes "Let's assume that ELOF can be discontinuous Then i draw a diagram of broken electric...

Homework Statement Good day everyone. I am studying Gaussian cylindrical surfaces. I have three questions: (1) Books would say that the electric field lines would emanate from the lateral side of the cylinder and that the ends will not contribute anything. I cannot understand this because...

Homework Statement On a long dielectric line a charge with density ##10^{-3}## is applied one half with positive charge and the other half with negative charge. Perpendicular to the first line and 5 cm away from it we have another line with the same charge density and also half of it is...

The electric field in some region is found to have a constant direction . What you coclude about the charge in the region...?? How can I draw the electric field lines..?? :/

Been reading laymen's books on general relativity and I'm in need some clarification! ... Line 1: The shortest path from a point 9.8 meters above the surface of the Earth to another point at the same location in space but 1 second later in time. Line 2: The shortest path from a point 9.8...

Hello experts! What is stubs in regards with transmission lines? I don't find any precise and point to point definition of it. Every where book tries to make us understand with a concept of 4 to 5 lines and this makes me confused. Please tell me the very precise and easiest definition of...

Homework Statement We are given a point A(1,1,1) and a vector v=(m-1,3m-5,2m-6). We are asked to write the parametric and continuous (I don't know if that's the appropriate term; in Spanish it's called "forma continua" but you'll see right away what I mean) equations of the line formed by these...

Looking to build a zip line with 4% decline for the kids with: Class 2 50' CCA syp Class II telephone poles sunk 6.5ft. 3/8" cable 7x19 Galzanized cable for guy wire and zip line. 1st zip: 100ft Starting at 26ft on a 6' hill->Ending at 22ft 2nd zip: 120ft Starting at 22ft -> Ending at...

Hello everyone , I googled for it but nothing came up, Where can I find that? Thanks in Advance ,

guys I need loads of help for this question(s)? what do i even do ?!? Sketch the curve y = lnx and find the tangent line to this curve at the point where the curve crosses the x-axis. Deduce that, for small delta, ln(1 + δ) ≈ δ . - I know what the y = Inx curve looks like but what do i do...

Hi, please could someone explain why the magnetic field is stronger at the poles of a magnet. I know that the field line density is strongest at the poles and more spaced out in the middle. I get that. I just wanted to know why the magnetic field is stronger at the poles than the middle of a...

Homework Statement Hello, I have a quick question about the following problem F = (2y+3)i+xzj+(yz-x)k and straight lines from (0,0,0) to (0,0,1) to (0,1,1) to (2,1,1) Considering C1 is the line from (0,0,0) to (0,0,1) C2 is the line from (0,0,1) to (0,1,1) and C3 is the line from (0,1,1) to...

Hello guys, i have saturated spectrum of Rb. My goal is to identify which lines i see. http://imagizer.imageshack.us/a/img835/8787/xvwr.png So from http://www.opticsinfobase.org/oe/fulltext.cfm?uri=oe-15-10-6293 I have identified that there are to 2 Isotopes: Rb85 and Rb85, further from...

1. The problem statement,ll variables and given/known data I have the first and second derivatives of a parametric function and the book is asking for when the slope of the tangent is vertical and horizontal. I get that horizontal is when dy/dx is 0. But what about vertical, is that dy/dx is 1...

Homework Statement Find the angle between two straight lines,##y=x## and ##y=2x##. Find the general formula for finding the angles. Homework Equations ##f(x)=mx+c## ##\tan(\theta)=\frac{opposite}{adjacent}## The Attempt at a Solution First I assign a value for x and calculate the...

I don't believe they are because the field lines don't have a representation such as flux but I want to be sure. Also are flux lines a vector quantity?

Homework Statement In triangle ABC, point L and M divides the sides AB and BC in the ratio 2:3 respectively. AM and LC intersect at point P. From point P a line parallel to BA is drawn intersecting at D. Find the ratio of AD:DC The Attempt at a Solution I have attached the picture of...

Homework Statement In the spectrum depicted bellow (see added picture) are spectral lines which resulted from emissions of a photon due to an electron decaying from a higher to a lower orbital in a Hydrogen-like atom (meaning- only one electron. No details about the nucleus) All lines in the...

I was told at school that when a hydrogen electron gains heat energy enough to excite it shifts to a higher energy level, then after a very small period it falls back to its ground energy level, that means all the energy it gains should be lost, but if that is true since hydrogen has an electron...

I need help understanding a certain problem. It basically stated: an airplane accumulated a positive charge, heading westward above the equator. Find the direction of the force (using the lame right hand rule thing). The problem I had was figuring out was whether the magnetic field would hit...

On an intuitive level, Why do stars show absorption lines? For example, the 121.6nm photon is produced when an electron falls into the lowest level of a hydrogen atom. A 121.6nm photon is absorbed by a hydrogen atom being kicked into an excited state, where it will eventually emit a 121.6nm...

Homework Statement This is the theory for a laboratory session. If we have two hollow cylinders, one with radius r1 and the other with radius r7, the center of the first one being placed at a distance d from the center of the second one, what are the surfaces having the same electric...

I don't know very much about differential geometry but from the things I know I think that the metric is somehow the quantity which specifies what kind of a geometry we're talking about(Though not sure about this because different coordinate systems on the same manifold can lead to different...

Homework Statement Consider the function f(x,y) = cos(x^2+3y). Write down the gradient of f. Then find the lines in the x-y plabe where ∇f = 0 Homework Equations ∇f = (∂f/∂x,∂f/∂y) The Attempt at a Solution -2xsin(x^2+3y) = 0 sin(x^2+3y) = 0 y = -(1/3)x^2 and...

I have a general gauss' law/electric field question. In calculating the electric field of a cylindrical shape, gauss' law can be applied to find that the Electric field only points aways from the surface of the cylinder (aka, in the s-hat direction). But this means that there are no field...

Hi everyone So I have this homework and I need some help. I did not know how to write the equations here in the topic so I thought the best solution is to upload a picture of the notebook page.

Homework Statement Homework Equations The Attempt at a Solution The given field lines are at a maximum distance exactly midway between the charges but I don't know which equation to use to find it. Any help is appreciated. Thanks!

Homework Statement Charges 4q and -q are located at the points (-2a,0,0) and (-a,0,0), respectively. Write down the potential θ(x,y) for points in the xy plane, and then use a Taylor expansion to find an approximate expression for θ near the origin, which you can quickly show is the...

Here are the questions: I have posted a link there to this thread so the OP can view my work.

Hey guys! First time posting on this site. Been reading for quite a while and really loving it! :thumbs:! I'm a chemistry student and reading my book in general chemistry I couldn't understand two things about Sommersfeld's atomic model. I believe i understand the whole concept but what...

Homework Statement In a question I was asked, assuming a spectrometer reading of Hydrogen produced two strong spectral lines at 656.3nm and 410.1nm. And also assuming the diffraction grating had 500 lines/mm What is the highest order of spectrum which can be fully observed , i.e value of m...

Hello Everyone! I am working my way through Gilbert Strang's book on linear algebra. I came across a set of solutions to the problems whose solutions are not listed in the book http://www.scribd.com/doc/86849289/1/Problem-Set-1-1-page-8. However, as I was working on the following question: I...

I have a question regarding world lines and Minkowski diagrams. I have been looking everywhere for an answer and can't seem to find one, and I would just like some clarification. So if we have a Minkowski Diagram, with a particular world line drawn out for, let's say a particle, is the world...

Homework Statement The figure shows a semicircle with radius 1, horizontal diameter , and tangent lines at and . At what height above the diameter should the horizontal line be placed so as to minimize the shaded area http://imgur.com/grrCqWF Homework Equations The equation of a...

I need help getting around this Calculus 3 problem. Any hints will be gladly appreciated: Find the radius of smallest sphere that is tangent to both the lines L1 : x=t+1 y=2t+4 z=−3t+5 L2 : x=4t−12 y=t+5 z=t+17

Homework Statement The equipotential curves in a certain region of an equipotential diagram in an xy plane are parallel to the y-axis and are equally spaced. The potential is increasing in the +x direction. Which direction would an electric field vector point in this region? Homework...

How to find the intersection point between two lines? line 1: r = (3,1,-1) + s(1,2,3) line 2: r = (2,5,0) + s(1,-1,1)

Homework Statement An atom or ion with one electron has energy levels E_n=-A/n^2. Tw neighboring lines in its spectrum at room temperature have wavelengths \lambda_1=97.5 nm and \lambda_2=102.8 nm. (Note that hc=1.240\times 10^{-6} eV m). (a)What is the constant A? (b) Identify the atom...

Homework Statement Use shell method to find volume. y=x+2 y=x^2 rotate about the x-axis 2. The attempt at a solution I cannot seem to solve this. I thought this was the way to solve it, but I don't understand if I am missing something crucial. This is how I set up the...

Homework Statement A light source at the origin of the O frame emits short pulses of light in interval of \tau as measured in O. An observer located at the origin of the O' frame which moves at velocity v with respect to O along the x-axis, receives these light pulses. Use a world line...

How can it be shown that $$16x\cos(8x)+4x\sin(8x)-2\sin(8x)<|17x|?$$ This problem arises from work with damped motion in spring-mass systems in Differential Equations. I have gotten to this inequality after some algebraic manipulation, but am completely stuck here. Here is the illustrative...

I was looking through a book on magnetism and it had the attached diagrams of field lines and stated that the classical diagram of field lines exiting the N pole and entering the S pole is incorrect. They claim their diagram is the correct representation of the magnetic field lines. Their...