What is Line: Definition and 1000 Discussions

Homework Statement [/B] Find the cross product equation for the line L that forms the intersection of the planes: A: 2x - y + 2z = 1 and B: x + y - 2z = 1. Homework Equations General equations for planes A and B: (a, b, and r are vectors). A: a dot r = 1 B: b dot r = 1 r = xi + yj + zk ...

Can anyone explain why a photon seems to travel in a perfectly straight 3D line over unimaginable distances? What exactly defines a straight-line? The concept appeals to Cartesian coordinate space. Is there any way to quantify the straightness of a photon path? Or, does the path taken by...

I just did this following exercise in my text If C is the line segment connecting the point (x_1,y_1) to (x_2,y_2), show that \int_C xdy - ydx = x_1y_2 - x_2y_1 I did, and I also noticed that if we put those points into a matrix with the first column (x_1,y_1) and the second column (x_2,y_2)...

Homework Statement I would like to define pressure loses through transmission line to the transducer. In transmission line I have a reducing union, filter and L pipe. How I can find this differences? In case of frequency my reducing union reduce pipe diameter 6 mm to 3 mm how i can determine...

Hello,Suppose I have a vector equation: \begin{cases} x=0+10t\\ y=0+10t\\ z=0+10t \end{cases} Which forms the symmetric equation \frac{x-0}{10}=\frac{y-0}{10}=\frac{z-0}{10} Now, I know the symmetric equations can be split up so that you can form the two planes whose intersection yields the...

Hello. I 'm looking for a line amplifier schematics working around 1.5 GHz to compensate coaxial ( RG59/CU) loss behind a L.N.A

This is an example at the beginning of the section on the Fundamental Theorem for Line Integrals. 1. Homework Statement Find the work done by the gravitational field \vec{F}(\vec{x}) = -\frac{mMG}{|\vec{x}|^3}\vec{x} in moving a particle from the point (3,4,12) to (2,2,0) along a piece wise...

This is a problem from a section on Line Integrals in my Calculus Textbook, I haven't studied any physics relating to E&M yet, and the solutions manual only gives solutions for odd numbered problems. Sorry, if I'm posting in the wrong forum, I hope I'm not. 1. Homework Statement A steady...

A straight line in 3 space can be described as A + Bt, where A is a position, B a direction, and t a scalar parameter. CAD surfaces can be represented in terms of polynomial functions of two variables (u and v) with the highest degree term being u^nv^n. The intersections can then be obtained as...

Hello, I would like to understand why "bushings" that are used as insulation for high power electric cables in transformers, and which are often made out of porcelain or glass, I would like to understand why they have this form of "skirts" ? Why aren't they just as a simple cylinder?

Can a line be parallel to itself?

When wave is reflected back means power is reflected back and not all power is consumed at the load. But I am thinking if I placed the load at the position of Vmax (of the stationary wave formed by the incident and reflected wave). Isn't that all the power will be dissipated at the load, so...

http://news.nationalgeographic.com/2015/05/150315-quadruple-quasar-mystery-space-astronomy/National Geographic quoting Dr Hennawi, the lead author of the Science paper, says it is a ten million to one chance to find four quasars so close together. How much more unusual is it that in the first...

I was reading a closed thread here about the length contraction being real or not. The best I could understand my self is that space is the one that contracts, the final post by an experienced forum member saying something like its the space-time that changes, it rotates. But I still have to...

I was reasoning about prandtl's lifting line theory. Now, a lot of books state that if the the circulation changes across the bound vortex filament a vortex sheet of the same intensity must be shed from the filament following the wake. Is this a consequence of the helmolzt theorem that forbids...

Homework Statement Given the polar curve r = 3\sqrt{\cos{2\varphi}},\ -\frac{\pi}{4}\leq\varphi\leq\frac{\pi}{4}. Find the area of the surface enclosed by the curve using line integral of the second kind. Homework EquationsThe Attempt at a Solution According to Green's theorem: if F(x,y) and...

The situation: I have a line represented in 3D space with XYZ coordinates. The line also has a M value for the distance from the start point in 3D. I have another data set that has "events" that I would like to find on my line. They have a distance (M) for the start and stop of the event...

We know that,the shape of electric field line in a cylinder under varying magnetic field is circle,and I wonder,what's the situation if it is a piece of metal with rectangular cross section? I think it might be something like superellipses.Can somebody tell me is it true or how to treat this...

1. A Magnetic field line has a length of 70,000 [Km], for this example all particles have an energy of 1.6E-27 [J]. Assuming all motion is parallel to the magnetic field line how long would it take to complete this cycle.2. M[Proton] = 1.677E-27 [Kg] , M[Electron] = 9.1E-31 [Kg] , E[kinetic] =...

Homework Statement Let C be the straight line from the point r =^i to the point r = 2j - k Find a parametric form for C. And calculate the line integrals ∫cV*dr and ∫c*v x dr where v = xi-yk. and is a vector field Homework EquationsThe Attempt at a Solution For parametric form (1-t)i + (2*t)j...

Ok I do not know if I am right about this but : if you have an AC 120 V 60Hz generator connected to a wire of Length L(1000KM) and Resistance R going to a motor down a well, to know if you will have Voltage loss you do λ = C / F C is the speed of Light = 299 792 458 m/s F is the 60Hz λ =...

Can anyone please tell me where I am going wrong? I am getting the incorrect answer for the Word Done should be: WD = q(3x^2-6y) ... Apologies for not changing it into the format on here - but for my revision I have pretty much done that myself.

I am confused with the classical approach of usage of a "transition dipole oscillation" in order to explain the broadening of spectrum of emission between energy levels. 1. If I understand it correctly then emission of photon is due to oscillation of a dipole consisting of an electron-proton...

Homework Statement Compute to three significant figures the wavelength of the sixth line in the hydrogen Balmer series. Homework Equations 1 / lambda = R * ( 1/ n_final^2 - 1 / n_initial^2 ) R = Rydberg constant = 10973731.57 m^-1 lambda = wavelength The Attempt at a Solution I set up the...

Homework Statement Use Green's Theorem to evaluate the line integral along the given positively oriented curve. ##\int_C y^4 dx + 2xy^3 dy ##, C is the ellipse ##x^2 + 2y^2 = 2##. Homework Equations Change of variables: ##\int \int_S f(x(u,v),y(u,v)) |{\frac {\partial(x,y)}{\partial (u,v)}}|...

Homework Statement How would I find the equation of a line which passes through A(x1, y1, z1) and is perpendicular to A(x1, y1, z1) B(x2, y2, z2), C(x3, y3, z3) Homework Equations Cartesian form of a line in \mathbb{R}^3 The Attempt at a Solution Not sure if this is right but would finding...

Homework Statement Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 1) Is the statement above the same as finding the area enclosed? 2) ##\int_C \cos ydx + x^2\sin ydy ##, C is the rectangle with vertices (0,0) (5,0) (5,2) and (0,2). 3) ##\int_C y^4...

Hello I want to obtain ABCD matrix element value.At first I tried to find A element value with boundary conditions but I don't know how can I find relationship between V(1)+ and V(1)- . Any help appreciate

Homework Statement Equations of the bisectors of the lines ## 3x - 4y + 7 =0 ## and ## 12x + 5y - 2 = 0## are ? Homework Equations Line equation is y = mx + c where m is slope and c is y interceptThe Attempt at a Solution Bisector is a line cutting equal angles between those 2 lines. But what...

Homework Statement If the line ## hk + ky = 1 ## touches the circle ## x^2 + y^2 = a^2 ##, then locus of the points (h,k) is a circle of radius : a h k 1/a Homework Equations NA The Attempt at a Solution Tried differentiating circle equation (Is differentiation of use here?, also don't know if...

In my textbook, its given that the equation of family of circles touching a given circle S and line L is ##S+\lambda L=0## So to find the equation of family of circles touching line L at point P(p,q), can i use the same equation taking S to be a circle of radius zero and center at P? That is...

Hello, I cannot find back from school, the formula to use: A 3 phases 220Vac system, no neutral, 3300W of pure resistance load between L2 and L3, the same load between L1 and L3, nothing between L1 and L2. What will be I1, I2, I3 the current in the 3 lines of the network? Thanks in advance -- Jmp0

Homework Statement Find the potential at a distance from a very long line of charge with linear charge density (charge per unit length) λ. I actually have this solved with the help of my book, but I need an explanation of the results. V = (λ/2πε)ln(rb/ra) Where the electric potential at rb...

Homework Statement a) Suppose that A,B,C,D are four "points" in a projective plane, no three of which are on a "line." Consider the "lines" AB, BC, CD, DA. Show that if AB and BC have a common point E, then E = B. b) From a) deduce that the three lines AB, BC, CD have no common point , and the...

Homework Statement Purcell 2.10 [/B][not the problem I'm asking about, but needed for Purcell 2.11 which I am asking about] A thin rod extends along the z axis from z = -d to z = d. The rod carries a charge uniformly distributed along its length with linear charge density \lambda. By...

Would it be correct to say that the distance between particular points is the same as a line? If so, does every possible line on a graph exist? Are the number of lines infinite?

This is a question I have been playing with this week out of curiosity but I keep coming up against brick walls and unenlightening results. Given the equation of an ellipse, say $$ x^{2} - xy + y^2 = 2, $$ I would like to find the equation of the line which passes through the major axis. I...

Homework Statement Plot the iA vs. vA characteristics for the nonlinear network shown in Figure 4.49. Assume the diode is ideal. The nonlinear network from part (a) is connected as shown in Figure 4.50. Draw the load line on your v i characteristics from part (a), and find iT Homework...

Is there an equation for say a line segment in 3D Cartesian Coordinates that is between these two points? Point One: x=0, y=0, z=0 Point Two: x=5, y=5, z=5 Does it involve inequalities?

I'm looking for how to mathematically relate X and Y, in such a way that the Chi-Squared per degree of freedom is minimised. However I can't understand how this would work, given that I'm trying to use known X,Y dX and dY (errors) values, to get the related gradient and intercept for the line of...

Having some trouble with this.. Need to find equation of a line with a slope of -1 that is tangent to the curve y=1/(x-1). So, rearranging slope formula as y=-1x+k and setting the equations equal, y=-1x+k=1/(x-1) y=(-1x+k)(x-1)=1 Here is where my multiplication is either totally wrong or I am...

Hey all, for some software I'm writing a sub problem of a bigger math problem I have is that I need to find the line of intersection of two planes, One can obtain the normal via the cross product but I am stuck at how to find a point on that line as they're seems to be too many variables...

Can someone please type out the line element for the Godel metric (including any and all c terms and any other terms that one might omit if they were using natural units to set terms like c = 1)? I ask this because different sources on line have it written out in different ways which look...

Homework Statement Here is the problem I am stuck on. I have checked my process multiple times, but have come up with the same wrong result. I would like to find out where by error of thinking lies. "An infinitely long line charge of uniform linear charge density λ = -1.30 µC/m lies parallel...

For an EM wave close to the transition frequency ##\omega_{21}##, we assume the dipole moment to be exponentially damped and oscillating: p(t) = p(0) e^{-\frac{\gamma}{2}t} cos(\omega_0 t) Why do we expect the electric field to be proportional to ##\dot p##? Taken from my lecturer notes on...

Homework Statement Let T : R2→R2, be the matrix operator for reflection across the line L : y = -x a. Find the standard matrix [T] by finding T(e1) and T(e2) b. Find a non-zero vector x such that T(x) = x c. Find a vector in the domain of T for which T(x,y) = (-3,5) Homework EquationsThe...

okay so as usual I am stumped ( I am not sure if I dislike math, or simply those who proclaim to be teachers of it. Spouting off steps is not the same thing as teaching ) Anyway, I have a problem that requires me to determine the equation of the line described: Through (6,-4), perpendicular to...

Since an accelerated frame is at rest in some inertial frame (MCRF) only at at a particular instance, I clearly have to use integration to calculate the total proper time elapsed for the accelerated frame. If I take an infinitesimally small spacetime interval along an arbitrary timelike path...

I know that for two points, the difference between them is a line segment lets say these two points are 'a' and 'b' respectively, so b-a = "new vector represent the line" In my textbook b-a=d*t -- where 'd' is a vector along the directon of 'b-a' and t is a parameter. does 'd' actually...

Hello! (Wave) I am writing a text in LATEX. Since the equalities I wrote are longer than the paper's size, I tried to break the line as follows, but it failed. \begin{multline} y'=y+4 \pi \cos(4 \pi t)y \Rightarrow y'=(1+ 4 \pi \cos(4 \pi t))y \cap \Rightarrow \frac{dy}{dt}=(1+ 4 \pi \cos(4...