Planes Definition and 523 Threads

The diagram shows two particles, A of mass 5m and B of mass 3m, connected by a light inextensible string which passes over two smooth, light, fixed pulleys, Q and R, and under a smooth pulley P which has mass M and is free to move vertically. Particles A and B lie on fixed rough planes inclined...

I am currently taking a 1st year introductory physics paper at university. I don't have a strong background in maths or science. Homework Statement A skateboarder with a total mass of 65kg is skating on a half-pipe ramp, as shown above. When he is at the bottom of the ramp he is traveling...

It's a pretty straight-forward question, and it got me confused since most articles on the internet mention planes of simultaneity in the context of inertial frames. So if rotating frames also have planes of simultaneity, what SR says about it and how does it differ from the planes of...

Homework Statement Aircraft A is describing a circular flight path in an anti-clockwise direction at 125km/h Aircraft B is flying the same path but in the opposite direction at 225km/h. If the radius of the flight path is 5km, calculate the acceleration of A relative to B when Aircraft A is...

find the general form of the equation of the plane with the given characteristics: passes through (0,2,4) and (-1,-2,0) and is perpendicular to yz-plane I know what the general form of an equation is, but I was wondering, do I set the direction vector to be <0,1,1> or <1,0,0>? How do I...

Homework Statement A trolley is of mass 20kg is pushed 35 metres up an inclined plane (to a height of 10m above ground level). The inclined plane is at arcsin(2/7) to the horizontal. A 100N force pushes the trolley to the top of the plane, the force being parallel to the inclined plane. The...

Homework Statement Take P;Q and R three points of R 3 not on the same line. If a = OP , b = OQ and c = OR are the position vectors corresponding to the three points, show that a x b + b x c + c x a is perpendicular to the plane containing P;Q and R The Attempt at a Solution I don't...

Does the distance traveled by an object sliding down an incline plane pertain to the base or the hypotenuse of the triangle? My guess is the hypotenuse, but I want to make sure in order to settle this matter once and for all.

I heard recently that the ecliptic is about 60 degrees out of alignment with the galactic plane, and was tilted up in the "front". Is that true?

1. Determine which of the three coordinate planes is closest to the center of the sphere(or indicate which planes are tied if two or more of the distances are the same) (s-7)^2+(y-7)^2+(z-7)^2=36 Homework Equations 3. Would i just try setting x,y,z in turns equal to 0 to find...

Homework Statement Determine the scalar equation of the plane that contains the line of the intersection of the planes x+y+z=4 and y+z=2, if the plane is two units from the origin. Homework Equations direction of intersecting line is M = N1 × N1 The Attempt at a Solution Let y= 0...

I having trouble understanding the difference between parallel and orthogonal in relation to finding the relevant line or plane equations. Example; Determine the vector and Cartesian line if: a) passes through (2,1,-3) and is parallel to v=(1,2,2) What would happen if it was...

From the book, given any two lines non intersecting lines in 3 space, any two planes each contains one of the lines can always make parallel to each other ( the two planes are parallel). The way the book described is that given two lines, you can produce two vectors V1 and V2, each parallel...

Homework Statement The acute angle between two planes is called the dihedral angle. Plane x−3y+2z=0 and plane 3x−2y−z+3=0 intersect in a line and form a dihedral angle θ . Find a third plane (in point-normal, i.e. component, form) through the point (-6/7,0,3/7) that has dihedral angle θ/2 with...

I know that when you are integrated over dA in the xy plane, for your polar coordinates, x = rcosθ and y = rsinθ. However what about in the xz and yz plane? I noticed in one of the textbook problems, where the integration is over an area in the xz plane, x = rcosθ and z = rsinθ. How did the...

Homework Statement Find the angle between the plane 3x+5y+7z = 1 and the plane z = 0. Homework Equations a.b=|a||b|cosθ The Attempt at a Solution Hi, I know that I need to have both these planes in the form (x,y,z) and then find the dot product to find the angle between them. The...

Homework Statement Two parallel plates having charges of equal magnitude but opposite sign are separated by 14.0 cm. Each plate has a surface charge density of 37.0 nC/m2. A proton is released from rest at the positive plate. (a) Determine the magnitude of the electric field between the plates...

Homework Statement Please disregard, sign error corrected in the cross product Determiner the line of intersection of the following two planes. Write the parametric equations for this line. 2x+y-2z=5 3x-6y-2z=15 Homework EquationsThe Attempt at a Solution First I crossed my normal vectors...

Homework Statement What is the equation of a line of the intersecting planes ##3x_1-2x_2+x_3=5## ##2x_1+3x_2-x_3=-1## Homework Equations The Attempt at a Solution I didn't know where to start but I started at trying to find the cross product of the planes (needless to say it didn't get me...

1. Homework Statement Find the cosine of the angle between the normals to the planes: x+y+2z=3 and 2x-y+2z=5 2. Homework Equations [/b] x+y+2z=3 and 2x-y+2z=5 3. The Attempt at a Solution All I know is cos θ= V * W / ||V|| ||W||

Homework Statement \vec{F}=(4x, 3y, 0) Find the flux over the part of the sphere centered at (0, 0, 0) with radius 4 between the planes z=-1.19 and z=0.87. The Attempt at a Solution \hat{N}=(x, y, z)/4 \int\int_{S}(4x, 3y, 0)\bullet([(x, y, z)/4])dxdy 0.25\int\int_{S}(4x^2+3y^2)dxdy The issue...

a) find the volume of the region enclosed by z = 1 - y^2 and z = y^2 -1 for x greater or equal to 0 and less than or equal to 2. b) would i split up the volume into two integrals, each integral for each z function and then add them together? I also don't know how to find the bounds...

Homework Statement http://img203.imageshack.us/img203/8536/capturezo.png Homework Equations The Attempt at a Solution I want to first make sure I understand the problem properly. Please verify each of my statements. If there is no force F acting on the (large) triangular block, then the large...

Dear All, I need you kind support in a problem, which I am unable to figure out. It is regarding thick lens. I am determining lens principal planes and radius using shaping factor and focal length. The forward problem I am using is, Focal length 1/f = (n-1)*[1/r1 - 1/r2...

Homework Statement I have two planes in R4, namely {[2, 0, 0, 1], [1, 1, 2, 0]} and {[-2, 0, 0, 1], [0, 1, -1, 0]}. Homework Equations The Attempt at a Solution Tried to row eliminate, didn't work. Tried figuring out a normal equation, but clearly that won't work in R4. Don't...

Please bear with my ignorance. I will try to explain the complete scenario . I have a 3D cuboid (with planes as front, back, left, right, top and bottom) and three spheres called s1, s2 and s3. s1's center is at (2,4,5) and radius is 2. s2's center is at (-2,3,2) and radius is 1. s3's center is...

I want to find the equations for the circles (formed on the planes) when a sphere cuts the XY, YZ and XZ planes. What I am trying to achieve is a software application that will have a 3D cuboid and inside this cuboid there will be many spheres. Now I want to find the circles created by these...

In the following two problems I am trying to get a deeper intuition of, the plane has 3 variables and is 3 dimensional and the hyperplane has four variables and is 3 dimensional as well. Can someone please show me why, practically, in the context of these problems? Question with hyperplane...

I have to understand some papers concerning pzt actuated membranes for a project and I keep stumbling upon d31 or d33 strain coefficients. Can someone please explain to me what do the 31 and 33 numbers refer to, regarding the geometry? I'm not sure I'm getting this so please feel free to ask...

Homework Statement I am given the following vectors : p = 3 q = 2 r = 5 2 4 3 -4 -3 -1 They ask to find these: 1. a normal to the plane containing p, q and r. 2. the distance from the origin to the plane...

Why would we want to transform a vector in our normal basis (xyz axes) to another basis? The only situation I can recall is when we are looking at a force applied on an inclined plane. Are there any other real life examples where this may be necessary?

Homework Statement 1. A vector u is given by u = λa + μb, where λ, μ are elements of ℝ. Calculate axu and bxu and show that: [(b χ u).n]/[(b χ a).n] = λ and [(a χ u).n]/[(a χ b).n] = μ (In any circumstance when I have omitted the underlining it is for convenience purposes, a, b...

Homework Statement Find all points on the surface at which the tangent plane is horizontal z=x3y2 Things I know: Tangent plane is horizontal then therefore the normal must be vertical in order to be perpendicular. Dot product of the tangent plane with normal is = 0 Normal...

Alright, I don't have a specific homework problem here, just a general question. I've attached two pages that I will be referencing. Figure 1. Inclined Plane As can be seen here, the FN = mgcos(∅) Figure 2. Banked Curve It seems as if the opposite is true here. FNcos(∅) = mg...

Find an equation for the plane through (−5, 1, 2) and perpendicular to n = 3 i − 5 j + 2 k. They say that : The plane has an equation 3(x + 5) − 5(y − 1) + 2(z − 2) = 0 What confuses me is why they switched the add/subtract signs and the order of everything when in my notes they...

How do you find the intersection of two planes in R3? The direction vector would be the cross product between the two normal vectors I imagine. So, how do I go about finding a point that lies in both planes so I can find the equation of the line? Thanks :)

Stress -- Cross-sectional and Inclined planes As per attachment... "On the cross-sectional plane mm the uniform stress is given by P/A, while on the inclined plane mm the stress is of magnitude P/A'. In both cases the stresses are parallel to the direction of P." The parallel part...

Homework Statement A plane is perpendicular to the line given by x=3+6t, Y=7+4t, and z=7-9t. What are the components of the normal to the plane Homework Equations The Attempt at a Solution I don't understand what the question is asking me all I have figured out that the normal...

In ℝ^{3}, how would I go about proving that two planes are parallel, given their equations? I know what the "word" parallel means, in the sense that two planes are always equidistant from one another, so that they must either never intersect, or that they must intersect at every point on their...

Homework Statement Two blocks connected by a cord passing over a small fictionless pulley rest on an double inclined plane (ie a traingle) with static friction coefficient of 0.5 and a kinetic friction coefficient of 0.4. The mass of block A is 100 kg (sitting at 30 degrees), while the mass of...

I want to test several different fluids on an inclined planes and figure out which one is the most slippery. What would be the most scientifically sound way to measure this?

I have two questions involving lines and planes. They're both fairly simple, but I'm stuck. I'm sure someone is going to point something out and it's going to make me smack my forehead. Homework Statement Where does the line through*(1, 0, 1) and (4,*−2,*4) intersect the...

Homework Statement Two semi-infinite conductor planes (like this ∠ ) have an angle β at a constant potential. Whats the potencial close to the origin? Homework Equations ∇²V = (1/r)(∂/∂r){ r ( ∂V/∂r ) } + (1/r²)(∂²V/∂\theta²) The Attempt at a Solution Trying for laplacian equation on...

Homework Statement The question is as attached in the picture.The Attempt at a Solution I understand and got the answer to part (a) but from (b) onwards I am completely lost. Here are my assumptions: 1)Edges of 'cube' are still of length a 2)Successive planes are parallelBut, there is some...

Homework Statement The planes 3x+2y+z=6 and x+2y+5z=1- intersect along the line (x+2)/2 = (y-6)/(-7/2)= z. A third plane passes through the origin and is perpendicular to the intersection of the first two planes, at what point do the three planes intersect? Homework Equations...

Homework Statement The question is attached in the picture. The Attempt at a Solution I have found the direction vector of the intersection line, but I have yet to find a point that lies on both planes... I've thought about having \hat{m} and \hat{n} as basis vectors, but i...

Homework Statement Consider two planes with normal vectors n1=<0,-1,-2> and n2=<-2,1,-2> For these planes and angle theta between them Homework Equations n1.n2=||n1|| ||n2|| cos(theta) The Attempt at a Solution I have gotten my answer for theta to be .729727 radians. Not sure why...

A cargo plane is flying horizontally at an altitude of 10.9 km with a speed of 850 km/h when a large crate falls out of the rear loading ramp. (Ignore any effects due to air resistance.) (a) How long does it take the crate to hit the ground? (b)How far horizontally is the crate from the point...

Homework Statement I got everything in the answer, just that my answer was 2∫ d∅ was from [0 to ∏]. Same answer, but different approach. The Attempt at a Solution How can the angle between 2 planes be greater than ∏? I took 2∫ d∅ from [0 to ∏] because I considered 2 cases, where y >...

Homework Statement A dot on the floor with a diameter of 2cm. A table that is at a distance of 46cm horizontally from the center of said dot. The table is 90cm tall. The meat of the problem: A ping pong ball rolls off an incline plane (a wooden board) that is on top of the table. The...