Planes Definition and 523 Threads

Is plane (1 1 2) identical to (-1 -1 -2), or are they just parallel?

Does anyone know of any interactive/good visual website for the adding and subtracting of planes? I'm doing the intersection of 2 planes right now, and I was just wondering if you had 2 cartesian eq'ns say 5x+2y+7z+1=0 and 5x-6y+8z-1=0, if you minus the 2 equations you'll have eliminated x, and...

Homework Statement (1 pt) Find the volume of the region bounded by the planes Homework Equations V = ∫∫7/4-6/4y-2/4xThe Attempt at a Solution Since y=x I found their values when z = 0. 6x+2x=7, x=7/8 y= 7/8 is the maximum value y will have in this integration as it decreases as x...

Homework Statement My professor gave us 4 points A(2,3,-5) B(-2,5,1) C(9,0,4) D(3,-5,8) So I must find an equation of the sphere that is tangent to 2 planes. These 2 planes are 18x + 39y - z= 158 18 x + 39y -z = -149 Homework Equations equation of sphere C(h,k,l) (x-h)^2 + (y-k)^2...

find the general equation of a plane that passed through the line of intersection (PQ) of 2x-7y+5z+1=0 and x+47-3z=0 find the equation of the particular plane through PQ which is parralel to the line x/-1 = (y-1)/3 = (z-3)/13 ok i think there is a couple of ways of doing this,this is the...

I was wondering, some of the things that define a Linear Space such as: v \in V then 1v = v or \vec{0} \in V such that \vec{0} + v = v They seem very obvious and intuitive, but, is there ever a time they break down in the Real plane? I think they might break down in the complex plane, but, I'm...

The Two Planes 2x-7y+5z+1=0 and x+4y-3z=0 intersect in a line PQ. What is the general equation of a plane through this line? Have done cross product of the two normals to get vector form of the line, and parametric x,y and z. Would like advice on what to do next, Thanks

Homework Statement The electric field equals 19j for points above plane 'r', -31j between the planes, and -19j below plane 's', where j is the unit vector in the +y direction and the fields are in V/m. Calculate σr, the suface charge density for plane 'r'. positive y- straight up positive...

Homework Statement Find value of k so that x+2y-z=0 x+9y-5z=0 kx-y+z=0 intersect in a line Homework Equations The Attempt at a Solution multiply l1 by 5 subtract l2 from 5l1 end up with: 4x+y=0 subtract l1 from l2 end up with: 7y-4z=0 i have no idea what to do from...

Hi, can anyone explain how miller indices can be determined for high index planes? For example, why is it that (544) = (S)-[ 9(111) x (100) ] I tried to figure it out but i could no find a pattern Thx in advance

Homework Statement My answer and the answer key in the textbook continue to differ by a constant d, which me and the book have opposites of. For instance, I found the vector to be y-z=1 but the textbook says y-z= -1 also, I got 7x + y - 11z = -5, but the book says 7x + y - 11z = 5...

Homework Statement Find symmetric equations for the line of intersection of the planes Homework Equations 5x - 2y - 2z = 1 4x + y + z = 6 The Attempt at a Solution I interpret this problem to say that I need to find a line of intersection of the two planes. I think I add them together and...

Homework Statement show that the plane 2x - y + 4z = 81 never intersects the line \frac{x-2}{3}=\frac{y-3}{2}=z-1 Homework Equations ?? The Attempt at a Solution I wanted to show that the line and the plane were parallel. So the unit vector for the line would be...

I am having a hard time visualizing the distance b/w two Miller planes. I found this article that has a brief explanation: http://www.mrl.ucsb.edu/~seshadri/2004_100A/100A_MillerBragg.pdf which derives the common formula for the distance, which can be used for diffraction/crystallography...

Homework Statement The planes 5x-2y-2z = -1 and x-4y+2z = 25 are not parallel, so they must intersect along a line that is common to both of them. The vector parametric equation for this line is ... The Attempt at a Solution Ugh... this is a doozie... So I started the problem by...

Determine whether the planes are perpindicular (-2, 1, 4) . (x-1, y, z+3) = 0 (PLANE A) (1, -2, 1) . (x+3, y-5, z) = 0 (PLANE B) Here's what I have figured out so far: Plane A passes through (1,0,-3) and is perpendicular to (-2,1,4) Plane B passes through (-3, 5, 0) and is...

This is just a basic incline plane problem. I know how to do it, but these sign conventions and vector issues are what confuse me. I know that I align my coordinate system so the x-axis is basically the surface the block is resting/moving on, the net weight vector of the block will be directed...

Just when I thought I got the hang of tangent planes and surfaces there comes a question I haven't quite seen before z = ln (x^{2}+3y^{2}) Find a normal vector n and the equation of the tangent plane to the surface at the point (2, -1, ln 7) So keeping the cartesian equation in mind: z =...

Suppose that F(x,y) = x^{2}+y^{2}. By using vector geometry, find the Cartesian equation of the tangent plan to the surface z = F(x,y) at the point where (x,y,z) = (1,2,5). Find also a vector n that is normal to the surface at this point...

Consider the system [S, L, P], where S contains exactly four points A, B, C, and D, the lines are the sets with exactly two points, and the planes are sets with exactly three points. This "space" is illustrates by the following figure: Here it should be remembered that A, B, C, and D are...

Atomic planes are defined as the reciprocal quantities 1/u' , 1/v' and 1/w' transformed to the smallest three integers (here the plane intersects the crystal lattice at the unit-cell axes u'a,v'b and w'c). My question is, why are reciprocal quantities used? This is something that has bugged...

Two inclined planes intersect in a horizontal plane. Their inclination to the horizontal is α and β. If a particle is projected at right angles to the former from a point in it so as to strike the other at right angles, then find the velocity of projection. Assume that the particle undergoes a...

Homework Statement Two planes of charge with no thickness, A and B, are parallel and vertical. The electric field in region 1 to the left of plane A has magnitude 3σ/(2*ε0) and points to the left. The electric field in the region to the right of B has magnitude 3σ/(2*ε0) and points to the...

Why haven't we seen commercial airlines attacked by missles yet? I can't imagine it's that hard to smuggle in an RPG. Many planes fly real close to the ground outside airport limits before landing. This seems like taking candy from a baby, yet we haven't seen it yet. I would imagine it would...

Homework Statement A 275 N box is sliding down a frictionless inclined plane. If the incline makes an angle of 30.0 degrees with the horizontal, what is the acceleration along the incline? I don't need to know how to figure out the solution to this problem - yet, atleast. Im trying to...

Homework Statement hello i just had a quick question, Supose there's a line in three space that is parralel to the xy plane but not any of the axes, what does this indicate about the parametric and symmetric equations in three space. Homework Equations The Attempt at a Solution I...

Homework Statement Solve the following systems and interpret the result geometrically 3x + 4y + 5z - 18 = 0 2x - y + 8z - 13 = 0 -x + 17y + 25z + 11 = 0 Homework Equations The Attempt at a Solution I've been working on this problem for a while, The first thing i did was find...

Homework Statement Can 1. three 2. four vectors in different planes add up to give a zero resultant? Homework Equations The Attempt at a Solution 1. Yes. 2. Yes. 1. suppose that we resolve the 3 vectors in i,j,k components. Putting each one of them zero in the...

Homework Statement A point charge q is located in the xy plane near two grounded conducting planes intersecting at right angles as shown in the Figure. The z axis lies along the line of intersection of the planes. Find and justify (mathematically show) the force acting on this charge q...

Two surfaces are said to be tangential at a point P if they have the same tangent plane at P . Show that the surfaces z = √(2x²+2y²-1) and z = (1/3)√(x²+y²+4) are tangential at the point (1, 2, 3). differentiate first then evaluate both at 1,2,3

Homework Statement Find all planes in R^3 whose intersection with the xz-plane is the lijne with equation 3x + 2z = 5 The Attempt at a Solution Very confused here, not sure how to start it. the xz plane is another way of saying y = 0... which I'm guessing is why the equation doesn't have a...

Homework Statement Ok, given 3 planes pi1, pi2 and pi3 with vector equations r.n1=0, r.n2=0 and (r-a).n3=0 respectively, where a, n1, n2, n3 are given vectors. No 2 planes are parallel and the third plane is parallel to the line, L, given by the intersection of planes pi1 and pi2. Consider the...

hi, i am interested in finding a website which has lots of questions (and solutions) on Newtonian mechanics to test my knowledge. things i had in mind include applications of F=ma,inclined planes, tension on ropes,springs etc. thanks

Homework Statement Find the acute angle between the planes Ax+By+Cz=D and Ex+Fy+Gz=H Homework Equations The Attempt at a Solution I have no idea

Homework Statement There's a pulley at the apex of an isosceles triangle, with a particle hanging from the string at each side (plane). Would the tension in this string be the same in this situation? Homework Equations The Attempt at a Solution

Homework Statement True or False: The intersection of two planes in R3 is always a line. The Attempt at a Solution I'm pretty sure that this statement is true because two planes can only be parallel, or they must intersect in a line because the are infinate. But I have no ideas on...

Given the parametric representation of two planes, through points P and Q respectively x = P + \alpha u + \beta v y = Q + a w + b z Or, alternately, with u \wedge v = A, and w \wedge z = B x \wedge A = P \wedge A y \wedge B = Q \wedge B It's easy enough to find...

I'm still not confident with these kinds of problems. Hopefully I got it right, but can someone double check my work? Thanks! Two parallel, infinite planes are separated by a distance d. Find the electric field everywhere (a) if both planes carry a surface charge density \sigma and (b)...

Homework Statement A woman pushes her 150kg motorcycle up a slope of 5 degrees with a constant speed of 2 m/s. She achieves this by exerting a force on the bike of 450N parallel to the slope. What is the magnitude of the frictional force acting on the bike? Homework Equations a=...

Our Milky Way is a spiral galaxy whose ecliptic plane is the same with the ecliptic of the Sun (or nearly). So do you think all other solar systems in the Milky Way also have the same characteristics?

I thought this might be a fun post (as this is my first) I want to know what others think about the existence of alternate , parralel universes'. Don't flame me...this is supposed to be fun ;)

Homework Statement I have to find volume of tetrahedron that is bounded between 4 planes. Planes are x+y+z-1=0 x-y-1=0 x-z-1=0 z-2=0Homework Equations \vec{a}=\vec{AB}=(X2-X1)\vec{i}+(y2-y1)\vec{j}+(z2-z1)\vec{k} \vec{b}=\vec{AC}=(X2-X1)\vec{i}+(y2-y1)\vec{j}+(z2-z1)\vec{k}...

Ok, I'm pretty much at whit's end trying to figure this review question out. Apparently my teacher forgot to mention that our book couldn't teach us everything we need to know for our test... Anyhow, the question is as follows, and I'm utterly at a loss as to what the answer is: Find the...

one type of aeroplane has a maximum acceleration on the ground of 3.5ms-2 a)for how many seconds must it accellerare along a runway in order to reach its take-off speed of 115ms-1? b) what is the minimum length of runway needed for it to reach this length? ummm, not entirely sure av...

i want the formula of Angles Between crystal Planes by knowning the information of Miller Indices of that planes? please help me

Homework Statement A skier of mass 70.0kg is pulled up a slope by a motor-driven cable. (a) How much work is required to pull him a distance of 60.0m up a 30.0 degree slope (assumed frictionless) at a constant speed of 2.00m/s? Given: \Delta r = 60m \theta = 30^\circ Mass...

Homework Statement Two planes r_1 and r_2 have the equations: r_1 = ( 1 - \lambda ) \underline{i} + ( 2 \lambda + \mu ) \underline{j} + ( \mu - 1 ) \underline{k} r_2 = ( s - t ) \underline{i} + ( 2s - 3 ) \underline{j} + ( t ) \underline{k} If a point lies in both r_1 and r_2 then...

so, for the very specific cases of linear systems i can identify what shape it will be after determining the eigenvalues, but i really do not know how to go about sketching the phase planes. can someone give me a method?

Hi everyone I hope I have the correct category for these questions! (I'm new to the forums). Anyways I'm currently in college studying to become a video game programmer, I've never taken physics before and I was doing fine in my course until we have started learning about Lines and Planes in 3D...

Homework Statement In this question, Earth is a plane described by the equation x + y + z = 18. Earth will be destroyed by an explosion that occurs at the point A = (1, 1, 1), also known as the “armageddon point”. It so happens that the school (considered as a point) will be the first...