What is Plane: Definition and 1000 Discussions

Homework Statement problem 1: given the straight line r whose equation is r=<3+2t, 4+2t, -1-t> 0.Determine A, intersection of the plane yz 0.1the parameter value at A is t= 0.2therefore A=(...,...,...) 1.we want to re-parametrize r (be u the new parameter) so that: 1.1the new...

Several companies have put forward plans for suborbital aircraft that use bouyancy to reach the edge of space. In fact, balloons can ascend to over 60,000 ft. Would it be possible to design an aircraft that uses bouyancy to ascend and then somehow convert to a glider to land unpowered, using...

find the values of k and m so that the line x+1/k = y-2/m = z+3/1 is perpendicilar to the plane through the points U(1,3,8) , W(0,1,1) , and v(4,2,0).PLEASE HELP ME THANKS ALOT :)

Algerie plane is missing

From Optics by Hecht He says "only a plane wave of infinite extent will propagate as a plane wave" What does it mean by " plane of infinite extent" in this context?

Homework Statement Find an equation of the plane that passes through the points (4,2,1) and (-2, 9, 6), and is parallel to the z axis. Homework Equations a(X-Xo) + b(Y-Yo) + c(Z-Zo) = 0 The Attempt at a Solution Okay so for this one, I first tried to make a vector out of the...

If the Parallel Axiom is just one of several possible assumptions, why is it that so many mathematical relationships seem to only be expressible in the Euclidean plane? Do planes with positive or negative curvature give analogues to the Agrand plane for complex algebra, or the Cartesian plane...

Homework Statement I was looking at the problem discussed in the thread below. https://www.physicsforums.com/showthread.php?t=502417 A block is initially kicked in the direction perpendicular to the downslope of the plane with initial speed V. The problem asks for the speed of the block...

How to define the plane of incidence for normal incidence of a plane polarized wave? Is the reflection coefficient defined by ordinary, extraordinary, or the combination of both waves? Thanks for the help!

I am reading the book, "Introduction to Plane Algebraic Curves" by Ernst Kunz - which the author claims gives a basic introduction to the elements of algebraic geometry. I need help with an apparently simple statement that I find confusing and puzzling. Theorem 1.3 and its proof reads as...

I am reading the book, "Introduction to Plane Algebraic Curves" by Ernst Kunz - which the author claims gives a basic introduction to the elements of algebraic geometry. The opening few paragraph of Kunz' text reads as follows:I am puzzled by Kunz statement: " \mathbb{A} (K) := K^2 denotes...

I was looking into what cylinders need pairing to make a set 0f 180 headers for an LS V8 engine. When looking the pairings shown below. LS firing order 1-8-7-2-6-5-4-3 Passenger (L) side = 1 3 5 7. Driver side (R) 2 4 6 8 1-8-7-2-6-5-4-3 L-R-L-R-R-L-R-L for a 4-1 header I get. 1-7-6-4...

Homework Statement determine the Cartesian equation of the plane through the points (3,0,1) and (0,1,-1) and perpendicular to the plane with equation x-y-z+1 = 0 Homework Equations The Attempt at a Solution Well I know the normal of the plane (a,b,c) dotted with (1,-1,-1) = 0...

My initial thought was that the plane wouldn't be able to take off. If the conveyor is moving in the opposite direction as the plane, at the same speed, then the plane wouldn't move relative to the ground (as if you're running on a treadmill, you're not actually changing position relative to the...

Homework Statement Obtain the differential equation of the family of plane curves described: Circles tangent to the x-axis. Homework Equations (x-h)^2 + (y-k)^2 = r^2 The Attempt at a Solution I tried to answer this question using the same way I did on a problem very similar to this...

Homework Statement A cylinder of mass M and radius R, with moment of inertia: I_c = \frac{1}{2}MR^2 rolls down without slipping through an inclined plane with an angle of θ, while pulling a block of mass Mb with an attached frame (of insignificant mass) which is connected to the axis of...

Dear Forum I'm an experimental photographer. During the last two years I've been developing a technique which I call light plane photography (LPP). LPP is a photographic technique that uses a plane of light and a camera to record photographs with unique optical effects. Here's three...

If a plane flies from point W due east to point E and then from E due west to W, does it take equally long? Why doesn't the rotation of the Earth makes it shorter going E to W?

Homework Statement A block takes 3 times as long to slide down an inclined plane that makes an angle of 30 degrees as it does to fall freely through the same vertical distance. Determine the coefficient of friction. Homework Equations F=μN The Attempt at a Solution I do not know...

Homework Statement Hey all! I'm new here but I think I'll like it. :) I have a question that I can't seem to figure out. Here is the question in short: GIVEN: A wheel of radius 1m on a vertical plane rotates with an angular acceleration of 4rad/sec2. The wheel starts from rest (ωo = 0)...

I get the theory: Fc = Ft + Fg Uniform circular motion, in the vertical plane. Fc = net force = centripetal force Ft = force of tension in the string Fg = force of gravity so at the top, with vector addition: Ft = Fc- Fg And if we define 'up' as positive, then should the equation look like...

given: a plane with normal N and a point on the plane P. a line from A to B that intersects the plane but is not coplanar. Find the point C on the line that is X distance away from the plane (along the plane's normal, meaning the shortest line that can be drawn from the point to the plane)...

Homework Statement Consider the plane 3x1-x2+2x3 = 0 in R3. Find a basis for this plane. Hint: It's not hard to find vectors in this plane. Homework Equations Plane: 3x1-x2+2x3 = 0 in R3. The Attempt at a Solution Let, A = \left[3,\right.\left.-1,\right.\left.2\right] \rightarrow...

The solution's form for the ODE $$\frac{d\vec{r}(t)}{dt\;\;\;\;} = k\;\vec{r}(t)$$ can be generalized like in this diagram: https://upload.wikimedia.org/wikipedia/commons/3/35/Phase_plane_nodes.svg Exist some program or some way of adjust some program of math for study the behavior of the...

Homework Statement We are given a point A(1,1,1) and a vector v=(m-1,3m-5,2m-6). We are asked to write the parametric and continuous (I don't know if that's the appropriate term; in Spanish it's called "forma continua" but you'll see right away what I mean) equations of the line formed by these...

Homework Statement If a particle moves in a plane so that its position is described by the functions x=Acosωt, and y= Asinωt, it is (A) moving with varying speed along a circle (B) moving with constant speed along a circle (C) moving with constant acceleration along a straight line (D)...

Homework Statement i can't understand how can the plane is parallel to vector b and vector c .. can you draw me a better diagram. i can't imagine Thanks Report Homework Equations The Attempt at a Solution

Homework Statement Let A, B, C be the vertices of a triangle in the plane and let a, b, c be respectively, the midpoints of the opposite sides. Show that Aa+ Bb+ Cc = 0 (all of them have vector signs on the left). Homework Equations definition of plane The Attempt at a Solution...

Homework Statement for this question (photo 1), i am not sure whether this is type 1 (as the type in photo 2) or type 2 ( as in photo 3 ). the question didnt provide a diagram, this is making me confused. so i did it another way on the right , (using pencil ). is my working acceptable ...

The linear combinations of V = (1,1,0) and W = (0,1,1) fill a plane. My question is how do i describe that plane? (not geometrically).

Could someone explain how angular velocity points perpendicular to the plane of rotation? I mean what is a physical explanation of this? (not mathematical) I mean for a rotating object it's easy to see that is has a tangential velocity that always points tangential to the direction of...

Homework Statement Find the distance from the point A = (1; 0; 2) to the plane passing through the point (1; 2; 1) and perpendicular to the line given by the parametric equations x = 7, y = 1 + 2t, z = t - 3. Homework Equations d = | (PS dot n)/|n|| The Attempt at a Solution Set n = <0...

Homework Statement My last inclined plane problem has a second part to it: There are some energy problems I need to solve. A double pulley consists of two separate pieces that are welded together; a hoop of radius 10.0 cm and a disk of radius 15.0 cm. The moment of inertia of the pulley is...

Homework Statement A double pulley consists of two separate pieces that are welded together; a hoop of radius 10.0 cm and a disk of radius 25.0 cm. The moment of inertia of the pulley is 0.160 kg-m^2. A 15.0 kg block (m1), on a 35.0° incline, is attached to the outer pulley by a massless...

Homework Statement A plane is given by the equation: 4x + 5y + 7z = 21 and a line by the equation r = (1,2,3) + \lambda (1,2,-2) where λ is real. Show that the line does not intersect the plane. The attempt at a solution So if I remember correctly, if n . a = 0 , they do not...

Homework Statement Let A=\mathbf{C}-{z:Re(z) and Im(z) are rational}. Show that A is a connected set. Homework Equations My book gives the definition of a disconnected set as a set that satisfies three conditions. A set A is disconnected if there exist two open sets U and V in \mathbf{C}...

Homework Statement A block is placed on a plane inclined at an angle θ. The coefficient of friction between the block and the plane is µ = tan θ. The block is given a kick so that it initially moves with speed V horizontally along the plane (that is, in the direction perpendicular to the...

I read the definition that a plane is a point and two vectors with the equation being plane sum = {OP + tv + sw} where v and w are vectors and t and s are real numbers. This is called the parametric description of the plane. I haven't seen the equation in this form before though. Can someone...

[b]1. A plane is aimed north and is traveling 851 km/h. A wind blows the plane from 40° S of E at 36 km/h. What is the plane’s resultant velocity? [b]2. I think the answer is 828.3 km/h at 88.1° East of North but I am not sure. Ay= 851 Bx= cosθ cos40=x/36 x=27.6 By=sinθ...

Hi, I have a situation like the following and I need to calculate the force as well as the sound pressure exerts on a rectangular object. If I have a sound source which is mapped on a 10cm x 10cm square plane, and the sound source generates for example 20Pa (N/m2) . The generated sound...

Homework Statement Find the distance from the point A = (1, 0, 2) to the plane passing through the point (1, 2, 1) and perpendicular to the line given by the parametric equations x = 7, y = 1 + 2t, z = t - 3. Homework Equations d = | PS * n/|n||, equation of a plane, The Attempt at...

Homework Statement Say we have the plane, x+2y+4z=8 (part of a larger problem) Homework Equations The Attempt at a Solution The vectors (8,0,0) and (0,0,2) both lie in the plane. They are linearly independent. But (0,4,0) lies in the plane and is not a linear combination of the first two...

Can someone please help me with this? I can't for the life of me figure out how to do these points. How do I line up the x, y, and z? I just can't grasp it and can't find anything online.

Homework Statement A 100 kg slender rod is lifted on the left end until the angle between the ground and the right end is 30 degrees. The right end is still in contact with the ground. The coefficient of friction between the rod and the ground is .5 and the length of the rod is 2.1 m...

Hi, Given a holomorphic function u(x,y) defined in the half plane ( x\in (-\infty,\infty), y\in (-\infty,0)), with boundary value u(x,0) = f(x) , the solution to this equation (known as the Poisson integral formula) is u(x,y) = \int_{-\infty}^{\infty} \frac{y\ f(t) }{(t-x)^2 +y^2} \...

I'm reading: http://www.feynmanlectures.caltech.edu/I_13.html#Ch13-S4 1. In the link it says: ##2\pi\rho d\rho## is the area of the ring of the radius ##\rho## and width ##d\rho##, if ##d\rho \ll \rho##. Why is this true?? 2. A bit further down in the text it says: Since ##r^2 =...

Homework Statement A uniform right circular cone of height h, half angle α, and density ρ rolls on its side without slipping on a uniform horizontal plane in such a manner that it returns to its original position in a time \tau. Find expressions for the kinetic energy and the components of...

Homework Statement While you were looking at the reflection of your feet in a plane mirror, you saw a dark spot on the glass. Assuming your height is 1.50 m, and that the eyes are located 0.1 m below the top of the head (a) What is the distance between the spot and the floor? (b)...

Say I have a plane, and it intersects with a [edited]cylinder*. What kind of method should I use to go about solving this? I've tried setting up a ##\int \int dA## situation, but wasn't sure that was applicable because it's in 3-space (also my plane is in terms of x y and z). I know it's...

Ok, so I'm really hoping someone can help me logic my way through this. I have a function to the effect of: ##r(u,v)=f(u,v)\hat{i} + g(u,v)\hat{j} +h(u,v)\hat{k}## I need to find an equation of a tangent plane at a point ##(u_{0},v_{0})## and quite frankly I'm at a loss on how to do this. So...