Lines Definition and 1000 Threads

when trying to find the distance between 2 skew lines i see how we can take the a vector between points on each and the cross product of the direction vectors to find the distance but is this looks only to be the distance from one line to a particular point on the other

Given a closed Riemannian manifold, a point P on it and a nonzero vector V in its tangent space, can you extend a geodesic in that direction of V indefinitely? I count looping back onto itself as "indefinitely". The theorem I have in my book only guarantees that this is possible locally near P.

Homework Statement Dear all, I have to find a fast way to compute changes in the level lines as the result of sudden changes in the local gravitational fields (2D space). (Caused by the destruction of a planet for example). I could recalculate everything but it takes too much time for the...

Homework Statement Calculate the wavelength of the Lyman-α line (the transition from the 1st excited state to the ground state) for (a) hydrogen atoms and (b) positronium e+e-, and explain the origin of their difference. In the light emitted from a star, a pattern of emission lines is found...

find the general form of the equation of the plane with the given characteristics: passes through (0,2,4) and (-1,-2,0) and is perpendicular to yz-plane I know what the general form of an equation is, but I was wondering, do I set the direction vector to be <0,1,1> or <1,0,0>? How do I...

Problem Description: A hiker is reading a compass under an overhead transmission line that is 5.1m above the ground and carries a current of 807A in a horizontal direction from North to South. Assume the Earth's field is of the order 0.5*10^-4T. A) Determine the magnitude of the field produced...

Imagine looking at a set of x-y-z axes, from directly along the z-axis. Say in this image, the road is the line z=0. Why is it, that only lines on or parallel to the z-axis get skewed? All the surfaces that are in or parallel to the x-y plane remain undistorted, and their angles are at 90...

Hello MHB, This is a problem from my book, calculate distance between line $$l_1: (x,y,z) = (1,1,3)+t(1,-2,-3)$$ and (hope it work's read $$l_2$$ cause I don't know how to write that in latex) I am stuck when I got $$l_2$$ in plane. I start with $$l_1$$ $$P=(1+t,1-2t,3-3t)$$ what shall I do...

Hello MHB, I am working with old exam and got one problem that gives 5 points (total 30 points) and it says line $$l_1$$ and $$l_2$$ gives of $$(x,y,z)=(1,0,1)+t(2,3,0)$$ and $$(x,y,z)=(2,0,-2)+t(1,2,1)$$ prove that $$l_1$$ and $$l_2$$ intersect each other. this is how I solved: There is an...

Hello. Assume an electron gun, as in CRT, made of plumbing copper instead of glass. Using magnetic scanning coils to move electron beam. Will the displacements of this beam be linear as if tube material was made of glass ? PS : this is not an exercise by though but a real problem I encounter in...

Hello MHB, I did find a problem in internet $$y=\frac{ln(x-5)}{x}$$ they say there is a vertical line at $$x=5$$ but should there not also be a vertical line at $$x=0$$? Regards, $$|\pi\rangle$$

Field lines do not intersect because at their point of intersection,we would get two tangents indicating two directions of electric field at that point. Suppose the two filed lines JUST touch at a single point. wouldnt there be only a single tangent at the point??

Here are the questions: Here is a link to the questions: Equation of tangent and normal? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Electric Grid Question -- Elevated Transmission Lines Hi, Our teacher gave to us an homework which is if we carry transmission lines at 20000 m (20km) high from Earth face, what is this application's benefits and harms? Can anyone help me? Already thanks for your replies...

Homework Statement The line x-2y+9=0 is tangent to the graph of y=f(x) at (3,6) and is also parallel to the line through (1,f(1)) and (5,f(5)). If f is differentiable on the closed interval [1,5] and f(1)=2, find f(5) A) 2 B) 3 C) 4 D) 5 E) None of these The correct answer is (C) 4The Attempt...

In the Midwest (Iowa, etc.), we get plenty of storms, mostly Winter, and power lines go down frequently. Someone is about to build a new high-power transmission line across my County (and too near my property!), and I can't figure out why it is not mandatory in the 21st Century that all...

Decide the angle between line $$x+2y-3=0$$ and $$-3x+y+1=0$$ we use ON-cordinate progress I know that their normalvector is $$(1,2)$$ and $$(-3,1)$$ but what shall I do next? Is this correctly understand Regards, $$|\pi\rangle$$

I read somewhere that a unique line connecting two points does not exist in higher than 3D, is this correct?

Hi to everybody. I´m reading a book about statics and I cannot understand this chapter. I have been calculating moments of forces in hundreds of problems, when I found a force acting on a body I needed to fix a coordinate system, then calculating the moment arms of that force around a point...

I see textbooks assign directions to magnetic field lines, for example north poles extending outward and south flowing inward. Are these directions correct or just a way to help tie the concept together and have just been arbitrarily picked much in the same way as conventional current?

Homework Statement I'm told to find the 2 points the two curves P and Q will intersect on and the parametric equations are: P (x=t, y=2t-1) Q (x=3t-t^2, y=t+1) The Attempt at a Solution I know I'm supposed to set x-equations and y-equations equal to each and solve so that...

Homework Statement Homework Equations The Attempt at a Solution I am not really sure how to optimize it from here. What should I be taking the derivative of the price function with respect to ??

So I'm a little confused. My question is: If a conductor is placed in an external electric field, do the field lines penetrate the conductor? My original thought was yes they do and then the induced field inside the conductor cancels out the external field so that the net field inside the...

1+50sinx/x^2+3 -5 < x < 5 3 zeroes: 0.02, 3.16, -3.12 Find the derivative and the slopes of the tangent lines. I need help with the last part. I found out the three zeroes by adding and subtracting pi from the equation at top by setting it to zero. Thank you!

Homework Statement This is taken from STEP II 2003 Q5. The position vectors of the points A, B and P with respect to an origin O are ai , bj and li + mj + nk , respectively, where a, b, and n are all non-zero. The points E, F, G and H are the midpoints of OA, BP, OB and AP, respectively. Show...

Homework Statement A line Ab inclined at 30• to the Hp has its ends a and b, 25 mm and 60 mm behind the vp respectively. The length of the top view is 65 mm and its vt is 15 mm below the Hp. Draw the projections of the line and locate its ht. also, determine the true length of the line Ab and...

I having trouble understanding the difference between parallel and orthogonal in relation to finding the relevant line or plane equations. Example; Determine the vector and Cartesian line if: a) passes through (2,1,-3) and is parallel to v=(1,2,2) What would happen if it was...

Homework Statement The Electric field lines in an X-Y plane are given in the attached image. The field is defined as E=αi(vector)y at x=0 and x=some distance along the positive X axis. α is a positive constant. Test for charges in the X-Y plane Homework Equations N/A The Attempt...

From the book, given any two lines non intersecting lines in 3 space, any two planes each contains one of the lines can always make parallel to each other ( the two planes are parallel). The way the book described is that given two lines, you can produce two vectors V1 and V2, each parallel...

In the figure below we have 2 hollow cylinder conductors. The red conductor has radius R1 and negative charge (Q1). We then introduce the blue conductor (radius R2), first connected to the Earth by a conductor thread. Then we disconnect the thread making the blue conductor charge be positive...

We know that hydrogen atom has got one electron.But If we look a hydrogen spectrum there are lots of spectral line. How can that be possible? Because in Bohr's atomic model the spectral lınes mean, electrons energy levels.It shows there is possible energy levels which electrons can...

I heard this question from my TA and was not satisfied with the answer. Can someone elaborate for me please? There are two infinite lines of current that are traveling in the same direction. By the right hand rule and ampere's law, we can calculate the magnetic field and calculate the F of...

On PF, to answer why atmosphere is transparent, users explained that atmospheric gases such as oxygen do not have absorption lines in the visible spectrum. On UColorado website, under Spectral Lines, they show that Oxygen has many visible lines in its spectral signature. This confuses me...

Hi PF, I want a good book to follow for electro magnetics , transmission lines and antennas etc. I would prefer the style of Richard G Lyons (DSP) or Hugh hildreth Skilling (Fundamentals of electric waves). I love the style in book 'Fundamentals of electric waves'. But it deals no...

Homework Statement Find the angle between a) The line L1 given by the equations y = 2z, x = 0 and b) The line L2 given by the equations x = 3z, y = 0. Homework Equations v.u=|v|*|u|*cos(θ) The Attempt at a Solution I know that I need to basically have a vector for each line to...

Hello, I hope somebody can give me a hint for this problem. Homework Statement A set of telephone connections should be installed in order to connect the cities A and B. City A has 2000 telephones. If every user of city A gets a direct connection to city B, 2000 lines would be needed...

I am having trouble understanding how the indexed union of ln in the first picture is equal to a subset of the plane; an element of it is a point on one of the lines. If I were to choose say 0 1 2 then the indexed union should be y=0 union y=1 union y=2. These lines would have no points in...

[FONT=Verdana]Show that one of the bisectors of the angles between the pair of straight lines ax2[FONT=Verdana]+2hxy+by2[FONT=Verdana]=0 will pass through the point of intersection of the straight lines ax2[FONT=Verdana]+2hxy+by2[FONT=Verdana]+2gx+2fy+c=0 if...

Hello, I got problem with A homework "find an equation of the tangent line to curve at the given point. $y=sec(x)$. $(pi/3,2)$ progress: $y'=sec(x)tan(x)$. So basicly that sec(x) don't say me much so i rewrite it as $1/cos(x)$ $y'=1/cos(x)•tan(x)$ now i can put $pi/3$ on the function to...

If each of the equations ax^2+2hxy+by^2+2gx+2fy+c=0 and ax^2+2hxy+by^2-2gx-2fy+c=0 represents a pair of straight lines , find the area of the parallelogram enclosed by them . Please help

In Jordan, Gauss-Jordan and Laplace it's necessary to miltiply a line by a constant, add the result to other line in order to obtain 'zeros' (to facilitate the process while using Laplace) or to obtain a identity matrix (Jordan and Gauss-Jordan). I take TOO long while doing this and sometimes...

Hello, guys I am struggling with solving the following ODE related to radial diffusion equation: du/dt=D*(d^2/dr^2+2/r*du/dr) For easiness I have attached the main m.file with general commands in Radial_diffusion.m pde1d.m contains function to be solved by ODE, and dss004.m contains...

1. Problem statement In a two-dimensional problem, σx=300xy and σy=300xy and τxy=0 at x=y=0. Determine lines of constant shear stress τxy in the x-y plane and plot them for τxy=100, 300, 400. Homework Equations dσx/dx + dτxy/dy + X = 0 [1] dτxy/dx + dσy/dy + Y = 0 [2] At least I think...

How would one derive the equation for (dP/dV)H? That is the partial of P over the partial of V, holding H constant. I've tried many different things, triple product rule, maxwell relationships, and nothing seems to work. I appreciate any advice.

Homework Statement Find all tangent lines of the graph f(x)=x+3/x that have a y intercept of 4. Homework Equations The Attempt at a Solution Assume a is the x coordinate of a point of tangency. Thus the point of tangency is (a, a+3/a). We know the tangent line must pass...

Suppose we have two charges in vacuum. They are positive and negative. If we want to draw the electric field lines around the negative charge. Do we draw the lines inward (negative) or outward (field lines produced by the +ve on -ve). I remember that free body diagram on a bidy does not include...

Hello all, and thanks again to all the help I've been getting with this book. This is a two part problem in Advanced Calculus of Several Variables, C. H. Edwards Jr. I have the first part and the second part should be easy, but I find I'm stumped. Since the second part builds on the solution of...

Homework Statement I am given the equation of two lines that are in three space. They are in the form of (X=, Y=, Z= ). The questions wants me to prove whether or not the lines intersect. Homework Equations The equations of the lines. It gives me just the points in the equation, but it is...

Hello I have a very basic question. I'm studying power cable engineering right now and I've learned about the role of insulation in a cable to reduce dielectric losses and charging current losses, but I don't understand what this means exactly. Here are my questions.. 1. Is the insulation...

Homework Statement A uniform electric field of magnitude 6.5 \frac{N}{C} passes through a circle of radius 12 cm. What is the electric flux through the circle when its face is perpendicular to the field lines. The Attempt at a Solution The only problem with this question is picturing the...