Planes Definition and 523 Threads

Homework Statement Consider a 2d potential problem for a region bound by 4 planes x=-1/2 x=1/2 y=0 y=1 There are no charges inside the bounded region. The boundaries at y=0 and y=1 are held at zero potential. The potential at the boundaries x=-1/2 and x=1/2 is given by...

In the book of the Dr. Ronald Askeland the problem about x-ray diffraction use the next planes indices to calculate the interplanar distance, but I don't understand why to use such planes indices? Are these planes all of planes in a cubic structure? (111) (200) (211)...

Hey all, I have a layman's question that's been bothering me for a while. As I understand it, the orbit of a given planetary body around a high-gravity object (like a sun) is determined by the balance between its tangential velocity and the force being applied on it by the high-gravity object...

Hello! I have a quick question regarding the intersection of three planes if the determinant is 0. If there are solutions, there will be an infinite number of solutions. One of the equations for the plane can be ignored as it is a linear combination of the other two, and can be ignored for...

Homework Statement Write down the general cartesian equation of a vertical plane (parallel to the z-axis), a non-vertical plane and a horizontal plane (parallel to the x; y-plane) together with their normal vectors. Find the cartesian equations of the line of intersection of the plane 5x + y ¡...

When light approaches and enters a material, why does all the reflection happen at the surfaces? I mean, light is coming at say, some crystalline solid. It hits the first plane of atoms and some is reflected. Some goes into the crystal and passes through the 2nd, 3rd, 4th,..., (n-1)th plane of...

This isn't exactly a specific question, but it is part of my homework (project). Anyways, suppose I have an inclined plane at 60 degrees. I can measure the mass of a freight car on top of the plane to calculate the force and final velocity of that car... I did this before in physics, and it...

I'd like some help understanding three things. - What is the topology of the Grassmann manifold or oriented 2-planes in R^4? - What is the Euler class of the canonical oriented 2 plane bundle over it? - I think that the Euler class of the normal bundle of an oriented surface in R^4 is zero...

Greetings, I am have a bit of a problem getting started on the following problem. The only thing that is confusing me is I am use to seeing a problem like this be perpendicular to 1 plane and not 2. The problem I am working with is as follows: Find the equation of a plane through the...

Homework Statement The vector -; = Xl + yj + zk, called the position vector, points from the origin (0. 0, o) to an arbitrary point in space with coordinates (x, y, z). Use what you know about vectors to prove the following: All points (x, y, z) that satisfy the equation Ax + By + Cz = 0, where...

Hey guys, I just have a general question, How would you find the equation of a line with just the equations of the planes intersecting. I know for the direction vector it would be the cross product, but for the other part of the equation r=ro +tv, the ro part i do not know how to find.

thought I understood equations of planes in R3 and their intersections, but apparently not. I'm very confused by what seems to be a basic problem: find a vector equation for the line of intersection of x + y + z= 0 and x + z = 0. Is x + z= 0 still a plane even though it doesn't have the...

Homework Statement Two bombers are flying 100m apart at the same speed. One is directly below the other. If the bomber above releases its bomb, will it hit the bomber below it? Homework Equations y - yo = -1/2gt2 x = vot The Attempt at a Solution I set the initial velocity to...

Homework Statement p1(x1,y1) , p2(x2,y2), p3(x3,y3), p4(x4,y4) are the vertices of a quadrilateral. Show that the quadrilateral formed by joining the midpoints of adjacent sides is a parallelogram. Homework Equations Midpoint = x1 + x2 / 2 and y1 + y2 / 2 The Attempt at a...

Homework Statement describe the set of points in space whose coordinate satisfy the given equation or pair of equations: (i) z=2y (ii) 3x=4y, z=1 if (i) or (ii) represents a line in space, give a unit vector that is parallel to the line. If (i) or (ii) represents a plane, give a unit...

Hi, I am having difficutly figuring out why the cross product of the normal vectors of each plane gives the direction vector of the line of intersection. Anyone care to try to explain? Thanks!

Homework Statement Two large planes have uniform charge density. Plane 1 is located at z1=-4 cm and has charge density σ1=-10μC/cm2. Plane 2 is located at z2=+6 cm and has charge density σ2=+20μC/cm2. a. Determine E(x,y,z) in the 3 regions. b. Determine V for all points. Choose V=0 at plane...

Homework Statement A flashlight located at the origin, (0, 0, 0), shines a beam of light towards a flat mirror. The beam reflects off of the mirror at (8, 4, 1) and then passes through (10, 8, 5). What is the equation of the plane that contains the mirror? Express answer in linear form...

Hi, I have been at this single problem for two hours with nothing to show for it. Find symmetric equations for the line of intersection of the planes. z = 3x - y - 7 z = 4x + 2y - 6 They also give me one of the symmetric equations, z/10. I have over 3 pages of work for this. I...

I recently heard from my friend that a flacon swoops down in a spiral (not spinning) motion to get a continuous view of its prey because it can see things clearly only in a 45-degree angle.(I don't know if this true, so please correct me if I am wrong.) I have even seen fighter jets doing the...

For a tangent plane to a surface, why is the normal vector for this plane equal to the gradient vector? Or is it not?

Homework Statement Find the distance between the planes 4x + 5y - 3z + 4 = 0, and -8x -10y + 6z + 12 = 0. Homework Equations V = (x, y, z) + Y(a, b, c) The Attempt at a Solution Okay, this problem has been driving me insane. Even though it's incredibly simple, and I know...

Homework Statement Ok I have a bunch of questions, please bare with me and i'd appreciate it VERY much if you could help me with these! 1. Assume that you are given the equations of three planes. Without solving the system, describe a "test" with rationale, that you could use to determine...

Hello, Given two planes, P1 and P2, I would like to determine their line of intersection L. I know three points that lie on each plane: (p1, p2, p3) for P1, and (q1, q2, q3) for P2. Based on what I am doing (triangle collision detection in 3D) it would be convenient to have L defined as a...

Homework Statement See first figure. Homework Equations N/A The Attempt at a Solution I think I got part a down(See second figure) but I'm confused as to how to approach part b. If it has to be parallel to line l then its going to be in the same direction as l. In other...

Hi I'm reading Lang's Intro to Linear Algebra Page's 30 -36 and I'd just like some input on whether I understand this or not. Basically my problem is with Planes but the parametric eq. thing is just clarification. Parametric Representation of a Line Basically, if you have two n-tuples (n=2 for...

I am trying to solve for the line that intersects any planes that fall under the arithmetic pattern of ax+(a+n)y+(a+2n)z=a+3n. The sample equations I've been using is (A) x+2y+3z=3, (B) 2x-1y-4y=-7 and (C) 6x-6y-18z=-30. Using a graphing program and Gauss' elimination I know it is a line where...

Homework Statement The point A(2,4,5) is reflected in the line with equation r = (0,0,1) + s(4,2,1) , sER, to give the point A'. Determine the co-ordinates of A'. Homework Equations 1. The equation of the line (parametric equations) 2. A (2,4,5) Dot Product, and distance from a point...

Homework Statement P1 = 3x+4y=1 P2 = x +y -z=3 Find the intersection. Homework Equations x = x0 +at y = y0 + bt z = z0 + ct The Attempt at a Solution I used a quicker method. I first did P1 x P2 and got its cross product <-4,3,-1> Then I followed what our teacher had shown us in class -...

I don't really understand what the dimension of a vector space for planes is. Is it 2 or 3 and why? What's the difference between the dimension of the plane as a surface (dimension of all surfaces is 2) and the dimension of plane in a vector space? Also, Wikipedia says that only planes passing...

Homework Statement Three-dimensional, euclidean space. We've got 2 non-parallel planes: \vec{OX} \cdot \vec{b_1}=\mu_1 and \vec{OX} \cdot \vec{b_2}=\mu_2. Find all the points Y such that Y lies on the first plane and Y+\vec{a} lies on the 2nd one. What did you get? Homework Equations Come in...

Homework Statement For my physics class we need to research on internet how torque and rotational mechanics has to do with planes. I already know a little about torque. I know that torque helps planes turn and spin (pivot). Is there anything else torque has to do with planes? Also, could...

Assume we have a plane of oscillating charges described by x=xoei(omega)t. The total field is given by E=- \frac{\etaq}{2\epsilonc}i\omegaxoei\omega(t-z/c) . (Can someone point me to a website where I can learn to type in these formulas and not not have them suck?) Ignore that weird looking x^o...

I'm a little uncertain concerning a math-question and would like to know if I've done anything wrong here, I do not have the correct answer which is why I'm asking. Homework Statement An arrow is shot in a straight line through the points (3, 4, -1) and (-2, 5, 2) and hits a plane...

Homework Statement Find an equation of a plane containing the three points (0, -4, 4), (5, -1, 1), (5, 0, 3) in which the coefficient of x is 9 Homework Equations N/A The Attempt at a Solution Totally lost on this guy. Prof didnt go over anything like this, nor tell us what the...

Homework Statement Find the vector equation for the line of intersection of the planes 5x−4y+z=3 and 5x+z=1 Homework Equations N/A The Attempt at a Solution I know this much. r=<__,__,0>+t<-4,__,__> Could someone explain to me what I'm actually doing? I understand how the two...

Homework Statement Find the vector and parametric equations for the line through the point P(-3, 3, -5) and the point Q(-7, 4, -1). Homework Equations N/A The Attempt at a Solution r= <__,__,-5>+t<__,__,4> The -5 and 4 are given. Heres what I have so far. r=<-3,3-5>+t<__,__,__> I...

please reply me i have a doubt. if two jet planes are flying together each producing 130 db sound. then what is the level of loudness heared by a person standing there. no other parameters are known. I have two concepts in mind ie) 1. every fundamental frequency produce hormonics and when two...

Homework Statement I'm looking at a problem where we have to draw the field lines above between and below two parallel planes going to infinity. Separated by distance D, both having equal positive surface charge density. 2. The attempt at a solution I know that there will be perpendicular...

If the line is parallel to the vector v = < -2,1,3>, what is the equation of the plane containing L and the point B = (-2,3,1) A) - x + y + z = 6 B) 3x - 2y - z = 4 C) x + 6y -11z = 5 D) x + 5y - z = 12 E) 2x + 10y - 19z = 7 I know we can get the equation of the line because we have a...

Most functions y=f(x) have tangent lines for any point x. Does a function z=f(x,y) have a tangent plane for any point x,y? And could you extend this to higher dimensions if necessary? (Tangent cubes? Tangent hypercubes?) Edit: Sorry, I thought I was posting in the General Math forum...

Dear friends, I am doing a Molecular dynamics simulations of a crystal. For this the initial configuration is FCC (face centered cubic) lattice. My problem is that I have to study the system for different orientations of the crystal i.e. (100) plane, (110) plane and (111) planes. For (100), the...

Homework Statement Surface (s) given by x^3*+5*y^2*z-z^2+x*y=0 question ask to find normal and tangent plane to S at the point P=(1,-1,0) then find vector tangential to curve of intersection of S and the plane x+z=1 at point P. Homework Equations The Attempt at a Solution So I started off...

Hey i need help with this question and i don't know wat to do after finding the normal vector of vectors a and s. And the normal vectors of vector t and b. Can someone help me please? the normal of s and a is (2,1,-3). and the normal of t and b is (-2,-1,3). is this right? Construct two...

Homework Statement In materials science right now we are learning about miller indices and crystallographic directions, including planes. What is the aspect ratio (height/width) of an AFM (atomic force microscope) silicon tip in the shape of a square pyramid where each face of the pyramid...

Homework Statement Question 1. Given position vectors OA : i+2j-k and OB: 2i+j+3k in a 3D Cartesian space with origin O of the points A and B. a) Find the scalar equation of the plane which contains A and which is perpendicular to vector AB. b) Find the shortest distance from the point...

i am to find the magnetic field between two infinite charge carrying plates, both a distance (d/2) from the x-y plane. current K=kx^. what i did was found the magnetic field of each plane with an amperian loop then added the found values. I am now wondering if it would have been better to use...

Homework Statement Given a common intersection point (3,4,5), find 3 different planes. Homework Equations None The Attempt at a Solution What I did is let a1x+a2y+a3z=a b1x+b2y+b3z=b c1x+c2y+c3z=c 3=Dx/D 4=Dy/D 5=Dz/D I set D=2, therefore Dx=6 Dy=8 Dz=10...

Homework Statement A point charge Q lies along the axis of symmetry between two half-infinite grounded conducting plates which form an angle theta (less than or equal to 90 degrees). a. What are the magnitudes and locations of the image charges? b. What is the total charge on the...

Homework Statement At ten am, a plane traveling east at 100km/hr is 500 km west of a jet traveling south at 200km/hr. At what rate is the distance between them changing at noon? Homework Equations The Attempt at a Solution 2aa' + 2bb' = 2cc' 2(300)(-100) + 2(400)(200) = (1000)c'...