What is Planes: Definition and 542 Discussions

The line of intersection of two perpendicular planes is r=(-1+5t)i +(5-t)j +(7-4t)k. One plane is 5x-3y+7z=29. Find the rectangular equation of the other plane. The Attempt at a Solution I think I need to find three points in the desired plane. (one point being (-1,5,7)?)

Homework Statement Determine value of k when thehse are perpendicular: [x,y,z] = [1+4s+kt, 2+2s+t, 7+2t] and [x,y,z] = [4,1,-1] + s[1,0,5] + t[0,-3,3] The Attempt at a Solution I learned that in 2 and 3D, two lines are perpendicular only if, after solving for the t in front of the...

Hello All, I need help in my Calc 3 class and I decided to come here for homework help. What I'm looking for is someone to just check my work for a couple of homework problems. I've already done the problems, I would just like my work checked. Anyone who helps, your kindness is greatly...

Homework Statement Find the volume of the solid bounded by the planes x = 0, y = 0, z = 0, and x + y + z = 9. Homework Equations . . . ? The Attempt at a Solution After drawing out the picture with z=0 I have a line going from 0,9 to 9,0 bounded by the x and y-axis giving me a triangle...

1. This is problem 2.10 from the book "Calculus of Several Variables by C.H Edwards": Let the mapping F: R2->R2 be defined by F(x1 , x2) = (sin(x1 - x2), cos(x1 + x2)). Find the linear equations of the tangent plane in R4 to the graph of F at the point (PI/4, PI/4, 0 , 0 ) The attempt...

Homework Statement On sheet Homework Equations On sheet The Attempt at a Solution On sheet

1. Two objects are connected via a pulley and some string. The 12 kg cart is on a frictionless 42 deg. incline while the 15kg block is on a horizontal surface having a coefficient of friction equal to 0.23. Determine the acceleration of the system of masses. 2. Fnet=ma 3. I first...

Homework Statement I am pursuing conceptual help regarding electric field due to uniformly charged planes. Homework Equations E=\frac{\sigma}{2\epsilon} The Attempt at a Solution I understand that a capictor has plates that are +/-Q. However, how would you calculate the elctric...

Homework Statement Two conducting planes meet at the origin at an angle \beta. Solve Laplace's equation in polar coordinates under the boundary condition that the potential is V_0 on the planes. Calculate the components of the electrical field near the origin. Explain how the charge density...

If I have cubic structure where plane is define by vector \rho and in z direction I have planes ...m-2,m-1,m,m+1,m+2... and if I have for example \sum_{m,\vec{\rho}}\hat{B}_{m,\vec{\rho}}\hat{B}_{m+1,\vec{\rho}} how to go with that in K-space? If I...

Homework Statement Consider three planes P1, P2 and P3 where a, b and c are constants. Plane 1 : x + 2y − z = 5 Plane 2 : ax + y + z = −2 Plane 3 : bx − 2y + cz = 11 1) Find the constants a, b and c such that the three planes intersect in a single point 2) For which values of d and...

I have to find two planes z=f_1(x,y)=a1*x+b1*y+c1 z=f_2(x,y)=a2*x+b2*y+c2 That satisfy: 1. both planes go through (-5,9,8) 2. the intersection line between the planes is located outside of the Cylinder x^2+y^2=4 3. the surface area of x^2+y^2=4 that is bounded between f1 and f2 is...

1. An 80.0 kg box is pushed up a frictionless incline. Hypotenuse = 10.0 m. Opposite = 7.0 m. How much work is done on the box moving it to the top?

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...

Find the parametric equations find the line through point (0,1,2) that is perpendicular to the line x=1+t, y=1-t, z=2t solution: a=<a1,a2,a3> 1+t=a1s 1-t=a2s+1 2t=a3s+2 a1=1/s+t/2 a2=-t/s a3=2t/s-2/s <1/s+t/s,-t/s,2t/s-2/s>*<1,-1,2> = 0 =>t=1/2 P(3/2,1/2,1) v=<-3/2,1/2,1>...

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...