Lines Definition and 1000 Threads

Homework Statement ax+by=k cx+dy=l ex+fy=m If in Exercise 12 k=l=m=0, explain why the system must be consistent. What can be said about the point of intersection of the three lines if the system has exactly one solution? Homework Equations The Attempt at a Solution ofcourse the system is...

HELP! Intersection of two lines (VECTORS) Homework Statement Find the common point of the lines r=i+j+k+x(j-3k) and r=i+y(k-j) Homework Equations The Attempt at a Solution If the lines intersect then there are numbers x and y such that i+j+k+x(j-3k)=i+y(k-j) The two...

Homework Statement In R3, consider the line l given by the equations {x=t,y=t,z=t} and the line m given by the equations {x=s,y=2s-1,z=1}. Let P be a point on l, and let Q be a point on m. Find the values of t and s that minimize the distance between the lines by minimizing the squared...

Homework Statement Draw a diagram to show that there are two lines tangent to both of the parabolas y = - x^{2} (1) and y = 4 + x^{2} (2) Find the coordinates of the four points at which these tangents touch the parabolas. Homework Equations y - y_{o} = m(x - x_{o}) The Attempt at a...

Homework Statement List the 4 properties and characteristics of electric field lines. Homework Equations I was not able to get them all and the ones that I did get I am confused that if it is really a characteristic or a property The Attempt at a Solution 1. Characteristic...

I tried asking a similar question earlier, but based on the answers I got I wasn't able to convey myself well. Here's Feynman's argument (at least as I understand it) for why, from a Quantum perspective, light (roughly) travels in straight lines from points A to B: 1) the photon will travel...

Which, if any, of the following statements about electric field lines is/are true? The electric field is always perpendicular to the surface outside of a conductor. - TRUE It is not possible for the electric field to ever be zero. - FALSE It is possible for two electric field lines to...

Homework Statement Determine equations of all lines the are tangent to y=x^2/(x-1) and that pass through the point (2,0). Homework Equations The Attempt at a Solution First I found the y' which I came up with y'=x(x-2)/(x-1)^2 next, let (a,f(a)) and put a to y'...

Homework Statement my textbook mentions the following as properties of lines of forces among other things They do not pass through a conductor. They contract longitudinally. They exert a lateral pressure on each other. I want clarification on these points i) Why lines of force do...

Homework Statement Use Gauss' law to explain why field lines must begin or end on electric charges. Homework Equations Gauss' law: \epsilon_0 \phi_E=q The Attempt at a Solution I'm not sure whether this solution is incomplete or inconsistent. First, I take a gaussian surface...

Hey all. I was wondering what the interaction between Electric and Magnetic field lines are. For example, when you hold up a magnet against a charged electrode. I tried searching in google, but everything just turned up one or the other or how a moving charge makes a magnetic field and etc.

Homework Statement [PLAIN]http://smartphysics.com/images/content/EM/03/h3_lineF.png A cylinder of radius a = 6.1 cm and height h = 9.7 cm is aligned with its axis along the y-axis. An infinite line of charge is placed at x=3.05cm where λ1 = -2 μC/cm and λ2 = 6 μC/cm at x=-3.05 cm. Point P is...

Homework Statement 1. The line perpendicular to the curve y = 2x^3 - x^2 + x - 3 at the point (1, -1) will intersect the x-axis at what point? 2. f(x) = |x^2 - 5| - x, for all x. Let g = f(f(f(x))), find g'(2). I tried just subbing in 2x - 1, the first derivative, to f(2x - 1) and...

Hi to everyone. I'm developing a puzzle game which involves some concepts of geometry. Suppose you have a rectangle formed by points A, B, C and D. Now, I add points X1 (lies on line AB), X2 (inside the rectangle) and X3 (lies on line AC). I'd like the output to be the two rectangles...

The problem is: Tangent Lines: Determine equations of the lines tangent to the graph of Y = x√(5-x²) at the points (1,2) and (-2,-2). Graph the function and the tangent lines. I have no IDEA where to go with this. I am taking calculus over the summer and we are in week 2 and I'm...

Homework Statement Find a differential equation whose solution is a family of straight lines that are tangents to the circle x^2+y^2=a^2 where a is a constant. The Attempt at a Solution So actually I'm stuck on the first part, coming up with such an equation. After some work I came up with...

How are power lines connected over canyons? Are they simply laid out on the canyon floor and then hoisted up and stretched to the towers? Just wondering. Thanks.

So I ran across this problem on the 'net and I can't determine "x". The arc length of the circle is 360. I added some other variable and took what I know about a circle and intersecting lines. I wound up with four variables and four equations. x = 1/2 (y + 67) w = 1/2 (z + 147) y +...

Here is the problem: http://postimage.org/image/1jy6nol5w/ Method 1: Steps 1. Calculate V(T1)=12*10=120V, V(T2)=10*10=100V 2. Since V(3)=10V and I(3)=1A, P(T3)=10W 3. Since not otherwise stated, Assume transformers are perfect. 4. So P(T3)= P(T2) = 10W 5. known...

Hi all, I am not sure if this is the right place to ask but I have two problems which I require enlightenment. The questions are, 1) Show that the intersection of two lines can be computed by rational operations. 2) Show that the intersection of a line and a circle can be computed by...

Homework Statement So I'm studying for my test. doing even and odd problems from the book. I wanted to see if this answer is right. Q: find an equation for the line in the xy-plane that is tangent to the curve at the point corresponding to the given value of t.Also, find the second derivative...

Homework Statement x1 = (0,0,4) + s(2,0,-1) x2 = (-4,2,2) + t(-5,1,1) Homework Equations The Attempt at a Solution First of all I find the common perpendicular (vector cross product) Make it unit Find a arbitrary line joining the two 2 lines (set s = t= 0) Then scalar...

Hi, I really tried to find some explanation about this notation S(x)-S(y), but I couldn't find any! I am reading a paper about Excitation of H_2 in Photodissociation regions, and it all the time say something like: "we find that the model can account for the first low H2 rotational line...

What determine the relative heights of the k-alpha, k-beta peaks in the X-ray production curve?

Homework Statement Yeah that always confuses me, why do books sometiems refer lines implicitly?

So I know that we can use absorption or emission lines from a star or object emitting light to determine the composition of that object. But what methods are used to confirm that? We've been doing this in class and it seems rather primitive to eyeball the lines and compare them with example...

Homework Statement <\body> <with|mode|math|\<b-phi\><rsub|B> = <big|oint>><with|mode|math|\<b-B\> \<cdot\> \<b-d\>\<b-A\>>\ \; magnetic flux is proportional to the number of field lines passing though the surface \; </body> <\initial> <\collection>...

Find the characteristic lines for the equation: 2 du/dx + 8x du/dt = 16x Here's my attempt a = 2 b = 8x c = 16x Using dt/dx = b/a = 8x/2 = 4x t = 2x2 + C C = t1 -2x12 Hence the characteristic is: t = 2x2 + t1 - 2x12

Homework Statement Two planes have equations 2x-y-3z=7 x+2y+2z=0 Find a vector equation for their line of intersection The Attempt at a Solution I haven't learned the vector product in class but read it and attempted it and got the direction vector 4i-7j+5k. However, I don't...

The lines (AC) and (BD) intersect at the point P(3,K) Show K=1. AC=(4,2) or (x,y)=(5,2)+s(4,2) BD=(3,-6) or (x,y)=(1,5)+t(3,-6) A(1,0), B(1,5), C(5,2), D(4,-1) [PLAIN]http://img840.imageshack.us/img840/6263/1894869.jpg

Hi, all: Say we have a bare-bones Vector Space v, i.e., V has only the basic vector space layout; no inner-products, etc., over a finite field . I think then , we can still define a line in V as the set {fvo: vo in v, f in F}, i.e., as the set of all F-multiples of a fixed...

Homework Statement Consider a uniformly charged half spherical shell. The total charge is Q and the radius is R. a) Calculate the electric field as a function of z for – 5R < z < 5R. b) Draw equipotential curves in the xz-plane for – 5R < x, z < 5R with at least 8 equallyspaced curves...

Homework Statement Take the Earth for instance, if I were to draw field lines, would it be field lines coming out of the mass or into the mass? I initially thought it would be going out because we could look at it as a "positive charge", but then I thought that was silly because gravity is...

Hi, I have a matrix V, which is a 5-by-2 matrix, where each row represents a point in the xy-plain. How can I connect these points together in MATLAB, please? Thanks in advance

some lines are called "resonant" Hi, I would like some explanation on a topic for which I do not find detailed literature online or in books. In photon absorption/emission processes by atoms, some lines are called "resonant" (for example, the 2P1/2 (or 2P3/2) to 1S1/2 transition of...

FIGURED IT OUT, PLEASE DISREGARD Homework Statement Find the shortest wavelength of the Lyman series for a triply-ionized beryllium atom (Be3+). Express your answer in nanometers using four significant digits. Homework Equations Rydberg's Formula: 1/\lambda=RZ2(1/n12 - 1/n22) The Attempt...

Homework Statement The spectrum of a hypothetical atom is shown in the figure. Three distinct spectral series are shown, with the center series corresponding to transitions to a final state of n_f = 3. (f is final) The indicated spectral line corresponds to the transition from an initial state...

shining white light through a gas of a vapourised element causes absorbtion lines to be created in the white light spectrum ie. there are dark lines running through the otherwise continuous spectrum and the position of these lines are unique to particular element. Why is it though that we...

Homework Statement The lines r=(2+2t)i+(3-3t)j+(4-2t)k and v=(4+2s)i+(1-6s)j+(5-3s)k are skew. Find the perpendicular distance between them at the point(s) where they cross over each other. Homework Equations The Attempt at a Solution Does this seem right...

The electric flux around a charge is represented by electric lines of force. But it is said that the electric lines of force is purely an imaginary concept to visualize a field. In the Gauss' law, using the formula q/epsilon we calculate the total number of lines of force. For a charge of 1...

Linear Algebra - Find the value of "a" such that 2 lines lie in a plane Homework Statement Consider the lines L1 and L2 with the following equations: L1: (x y z)=(7 4 −4)+t(2 2 −2) L2: (x y z)=(a 4 −4)+s(−3 2 −2) Find the value of a such that L1 and L2 lie in a plane. They also gave...

I understand why a ball's velocity vector is reflected across the line normal to the wall when it hits the wall. Why does this happen with light and a mirror? What is happening atomically for an atom to take in a photon and spit it out across the normal line?

Homework Statement Let f:\mathbb{R}^2\to\mathbb{R} be continuous everywhere except, possibly, at the origin. Furthermore, for any point p\in\mathbb{R}^2, let s_p:\mathbb{R}\to\mathbb{R}^2 be defined by s_p(t) = tp. Now assume that f\circ s_p is continuous, as a function...

Two tangents to an ellipse meet at a point T, find the coordinates of T. The two equations are (bcosΘ)x + (asinΘ)y= ab (-bsinΘ)x + (acosΘ)y= ab This has been really frustrating me as I feel it should be simple, but with the trigonometric...

Hi everyone, My data consists of road accidents and spatial covariates. Originally i wanted to apply an inhomogenous Poisson process with covariates. Then I realized that the accidents cannot occur everywhere in space, but only on roads. I found an example, that is quite similar to mine. it...

Where is it writ that forces must act in straight lines?

I am unable to comprehend the proof for tangent line to conics. Here is the proof as per the book (Multiview Geometry by Hartley and Zisserman). Everything is in homogeneous coordinates. The line l = Cx passes through x, since lT x = xT Cx = 0. If l has one-point contact with the conic...

I have a multi-lined coloured plot in which I need some lines represented by dashed lines ('linestyle', ':') and I also need my plot to be quite a high resolution (dpi) for publication reasons (print -r600 -dtiff myfile.tif). So this works fine but when I open the tiff file with high resolution...

Homework Statement Determine the magnitude and direction of the electric field at point 1 in the figure. Homework Equations E=\frac{QK}{r^2} V=-\frac{QK}{r} The Attempt at a Solution \int E dr=-V When I take the derivative of both sides of this relation wrt to R, I get...

Homework Statement You are given the two lines with the following parametric equations: L1: x = 4 + 2t y = 4 + t z = -3 - t L2: x = -2 + 3s y = -7 + 2s z = 2 - 3s Both s, and t are elements of a real number. Determine the coordinates of P1 that lies on L1, and P2 that lies on...