Planes Definition and 543 Threads

How to find (equations of) two perpendicular planes intersecting to a plane (say 3x+y+z=10) in a point (say 1,2,5 ). All the three planes are perpendicular to each other and intersecting at a single point (say (1,2,5) in this example) If possible explain it in vector form and non-vector...

I am trying to understand the behavior of bolt in different plane. My doubt is when shear force acts on bolts in 2 different plane simultaneously, does it share the shear force (F/2) or each bolts experience the total force (F). I am sure that if there is a bolt pattern on the same...

Homework Statement 2x-y-z=3 and x+2y+3z=7 Homework Equations The Attempt at a Solution Im stumped on this problem because initially i thought all i had to do was make z, or another variable zero and then just solve. However, it then turns into a nasty problem. Most of the...

urgent, intersection of two planes Homework Statement Find the equation of the intersection between 2x + 3y - 4z = 12 and 5x + 2y + 3z = 7. Homework Equations none. I don't know how to use cross products, but is there another way? The Attempt at a Solution I don't know...

Homework Statement Hi guys, I was helping a friend in grade 12 with his Linear Algebra, when I got stumped on some questions I wasn't quite to sure of. I forgot some of my old linear algebra so I need you guys to help me out:) Here's the question: 1)The two line with equations L1: r =...

this might be a dumb question , so if I roll 2 cans down a ramp one heavier than the other one they will obviously accelerate at the same rate but when they get to the flat land will the heavier one go farther because it has more mass to over come the drag or because it has more kinetic...

okay i came up with doing the gradient of the ellipsoid. Then set that equal to the vector, <4,-4,6>. I solved and got x,y,z = 1,-2,1 I looked at the answer key and it said (1/3) (1,-2,1) Does anyone know where the 1/3 came from?

Hi, I am currently doing a practice test for my final exam coming up, I am wondering anyone can double check the questions to see if i did them write, below is a picture of the questions, the answers i got are listed at the bottom, If you could, please post whether you agree with my answers...

Homework Statement 1. Find the distance betwwen the parallel palnes: a) x + y + 2z = 4 and 2x + 2y + 4z +11 = 0 b) ax + by + cz + d1 = 0 and ax + by + cz + d2 = 0 2.Find the equations of the two planes which are parallel to 2x - y + 2z = 5 and 2 unit from it Homework Equations...

Vector Planes & Orthogonality -- Help! I must be doing something really stupid, and I'll kick myself when you point it out, but I'm having difficulty with this question: Find the unit normal to the plane x + 2y – 2z = 15. What is the distance of the plane from the origin? OK, so I know I need...

Homework Statement Point A (3,2,-1) is equidistant from two planes (parallel), known as P1 and P2. P1 has the equation 2x-y+2z+4 = 0. Find the equation of P2. Homework Equations D = abs val(ax_o + by_o + cz_o + d) divided by sqrt (a^2 + b^2 + c^2) The Attempt at a Solution I...

Homework Statement i have to write this physics paper on the aerodynamics behind the flying of a paper plane. what laws are being applied to make it fly? Homework Equations The Attempt at a Solution

Hello. I've just been curious as to the answer to this question. Modern aerofoils are fine due to the geometry that allows for a pressure difference between the upper/lower surface. But as I remember WWI planes, they all have 4-5 levels of straight wings. Does that serve the same purpose? How? I...

Homework Statement How do I determine the distance between the parallel planes 2x-4y+ 2z = 5 and -2x+4y-2z= -9: ___? Homework Equations The Attempt at a Solution I got 1/4, but I think that is wrong. Any help would be great!

Homework Statement Show that the two planes are neither coincident, parallel, nor distinct. Identify, geometrically, how the planes intersect and determine the angle between the two planes to the nearest degree. \pi1: x + 2y - 4z + 7 = 0 \pi2: 2x - 2y - 5z + 10 = 0 I found the normals...

Mt Redoubt erupted 4 times last night (March 22) , resulting in plumes of fine, abrasive ash that has grounded flights in and out of Alaska...

Hi guys, I am sort of new here. So I am not pretty sure if I am to post this question in here. I am a software programmer and I need to write a class for defining a plane. I came across the plane in its normal form nx+ny+nz+d=0 I need to feed in the values of the plane from another...

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