What is Plane: Definition and 1000 Discussions

Homework Statement What's the vector equation for a plane which contains the point ##(-2,2,1)## and whose vectors ##(1,1,2)## and ##(2,1,-1)## are parallel to it? Homework Equations I think the relevant here is - The plane equation. The Attempt at a Solution [/B] We can go through...

Homework Statement A Jet is heading due east: its nose points towards the east direction, but its trajectory on the ground deviates from the east direction due to a sideways component of the wind. The plane is also climbing at the rate of 100 km/h (height increase per unit time). If the plane's...

A bit of unsual scenario, I need to divide a video projection beam horizontally into two. Since the splitted beams in my diagram are treated as a separate beam they have to have their focus plane changed. Is that possible to do and how would one do it? http://image.ibb.co/jAu9x7/9241421.jpg If...

Homework Statement I am reading the book of Gerry and Knight "Introductory Quantum Optics" (2004). In page 60, Chapter 3.7, there is two equation referring Fourier Transformation in the complex plane as follows: $$g(u)=\int f(\alpha)e^{\alpha^{*}u-\alpha u^{*}}d^{2}\alpha, (3.94a)$$...

In order for a conventional telescopic riflescope to function, it must invert the image two times. As a result, the light-rays traveling through the tube must meet at two focal points. With my limited knowledge of optics, i assume that parallell light going in through the objective will meet...

Homework Statement I am working through problem #1, a-c. Homework Equations The main equations are dx/dt=Ax, (A-rI)v=0, and det(A-rI)=0. The Attempt at a Solution [/B] Here is my attempt. I am fairly confident in my answer to A. I'm less sure on my answer to B, however it is the same as...

Hi everyone, I am new and I hope I'm putting this in the right section. I am currently a Sophomore in High school and I am building a wind tunnel. It's not for a class but rather its is like an independent study. I have been into planes pretty much all my life and I am hoping to get a pilots...

The situation: The mass is pushed up an incline with an angle of 1 degree with an initial velocity of 1 m/s, and it comes back down to its original position. The questions to answer: What is the total distance the object travels on the frictionless inclined plane? How long will the object...

Homework Statement Two bodies with mass m1 and m2 are tied together with an inexstensible and massless string rolled over a massless pulley put at the top of the incline with angle 30 . m2=5 kg which is on the incline is blocked and T=10 N . m2 is let loose and the system starts moving freely...

Homework Statement Find the scalar, vector, and parametric equations of a plane that has a normal vector n→=(3,−4,6) and passes through the point P(9, 2, –5). Homework Equations Ax+By+Cz+D=0 (x,y,z)=(x0,y0,z0)+s(a1,a2,a3)+t(b1,b2,b3) x=x0+sa1+tb1 y=y0+sa2+tb2 z=z0+sa3+tb3 The Attempt at a...

I continue to be occupied with the first chapter of Lessons on Particle Physics by Luis Anchordoqui and Francis Halzen. The link is https://arxiv.org/PS_cache/arxiv/pdf/0906/0906.1271v2.pdf. I am on page 24, where they derive equations 1.5.67, which are: ##(\gamma^\mu p_\mu-m)u(p)=0## and...

Homework Statement A 24 kg object is placed at the top of an incline with height 500m and length 375m. The coefficient of kinetic friction is 0.600 1) Find the acceleration of the object. 2) Find the speed by the time it has reached the bottom of the inclined plane. Homework Equations F_g =...

Homework Statement Homework Equations inertia equations The Attempt at a Solution I think the answer for this is B) or D) but I am not sure what the sentence "a special solid cylinder in which the density is proportional to the radius" means... The solid sphere has little inertia because...

Homework Statement Charge -q placed in front of an infinite plane of charge density σ To show the oscillatory motion of the charge -q It is allowed to impinge through charged plane Homework Equations Electric field in front of a charged plane is σ/2ε0 The Attempt at a Solution Force...

Homework Statement Obtain a 4×4 projection matrix that maps ##ℝ^3## to the plane 3x + 2y = 1. Assume that the centre of projection i.e. eye is at (0,0,0). The problem that my problem is strongly based on and its solution are #3, here. (I'm referring to the first way of solving the problem in...

Morning mates, I've peformed Galileo's experiment with inclined planes, using a ramp of 88cm (divided in 4 parts of 22cm), inclined by a height on the right-edge of 4cm. I've measured the following, 1/4 of the ramp (22cm): 1.75s (error of 0.1s) 1/2 of the ramp (44cm): 2.70s (error of 0.1s) 3/4...

Homework Statement A plane is to be used to drop emergency medical supplies (encased in a crash-proof container) to campers in Northern Ontario. The campers are in a clearing. The plane will approach the clearing at an altitude of 150m while flying level at 40m/s. a) Why can't the pilot wait...

Homework Statement A plane, diving with constant speed at an angle of 53 degrees with the vertical, releases a projectile an altitude of 730m. The projectile hits the ground 5.00s after release. A plane, diving with constant speed at an angle of 53 degrees with the vertical, releases a...

Hello, in geometric optics people usually say that the refraction of light beams due to a thin lens can be handled by introducing a hypothetical plane (the so called principal plane) at which all the refraction can be considered to happen. But most books only picture the situation for symmetric...

Hello, I have an issue regarding a constraint related to an angle: Suppose I have masses 'A' and 'B' on an inclined plane ( of mass 'C') attached by a pulley. I place my origin as shown and I want to find a constraint relating angle β. so, I saw my classmate writing as follows to find...

Homework Statement I have the inclinination i which is the angle between the orbital plane and the plane of the sky, i [0,pi/2] if it is in the direct sense ans [pi/2, pi] in the indirect, so here i have an angle i=40 in the direct sense how can i calculate the i in the indirect sense Homework...

Homework Statement Let P(W) be a projective space whose dimension is greater than or equal to 2 and let three non-colinear projective points, [v_{1}],[v_{2}],[v_{3}]\in P(W) . Prove that there is a projective plane in P(W) containing all three points. Homework EquationsThe Attempt at a...

Homework Statement On a plane tilted at the angle of 30 degrees with the horizon lies an object, whose weight is equal to 1.4 kg. The coefficient of friction between the object and the plane is equal to 0.2. Find acceleration. m = 1,4kg; (weight) Angle (A) = 30 degrees. COF µ = 0,2 Ff -...

Homework Statement A plane is taking off from an airport directly west of the airport it wishes to touch down in. The plane in still air can travel with a constant speed of 730 km/h. If a wind is blowing constantly at 92 km/h [45° S of E], at what angle must the plane fly to compensate for the...

Hi, I appreciate any help. Thanks in advance! Homework Statement The image shows the top view of the set-up. Basically, it is a cylinder (resting on a horizontal plane) with two rods on either side attached in line with the centre of mass of the cylinder. Two pieces of string are then taped...

Homework Statement At what height above the Galactic plane are there the same amount of thin and thick disk stars. Information given: 1) Thin-to-thick disk star counts is 15-to-1 (by volume density) 2) The scale height of the thin disk is 0.3kpc 3) The scale height of the thick disk is...

Homework Statement A point charge q is located a distance d meters from an infinite plane. Determine the electric flux through the plane due to the point charge. [/B] Homework EquationsThe Attempt at a Solution I consider another infinite plane at a distance d in the opposite direction. Now I...

I'm looking for a diagram or animation that shows the vector potential A (in the form of arrows or whatever) superimposed on the E and B fields of a plane EM wave. Since A is not unique, maybe two or three versions of the diagram (including one with Coulomb guage). An animation with a slider to...

This has been a real famous analogy and I understand it, except the fact that the balloon surface is a 2D structure. How is it possible to depict a 3D universe on a 2D plane ? What happens when we work with stars at multiple planes ?

$\tiny\textit{243.12.7.12}$ $\textsf{Write the equation for the plane through points}$ $$A(-3,8,1),\, B(5,-7,-18),\, C(-1,-5,24)$$ ok, tried to follow an example of cross product but.. $$\displaystyle\vec{AB}\times \vec{AC} = \begin{bmatrix} \textbf{i} & \textbf{j} & \textbf{k}\\ \, 5 &-7...

Homework Statement Vectors A and B are in the xy plane and their scalar product is 20.0 units. If Amakes a 27.4° angle with the x-axis and has magnitude A=12.0 units and B has magnitude B= 24.0 units, what can you say about the direction of B? Answer: 113.4° and 301.4°The Attempt at a Solution...

Hi, If I have a 3D plane Ax+By+Cz=0, and I know the line equation of its intersection with the reference plane, what is the maximum inclination a point can have and what is its equation in the xy plane? Is it perpendicular to the intersection? That is , if the slope of the intersection line...

I'm interesting in about possibility to express a tetrad of a rotating matter in neutron star (in some approximate known metric, where shape of star is unchanged - Lense-Thirring metric) outside of the equatorial plane. My idea is: I start from Locally Non Rotating Frame (LNRF) in equatorial...

Homework Statement g = ##10m/s^2## ##\sqrt{3}## = 1.7 Determine work by the 20N force Homework Equations for an inclined plane: W = ((F+mgsin30)-(mgcos30)μ)s -> (Fx-ff)*s for object pulled with angle: W= (Fcos60-(mg-Fsin60)μ)s -> (Fx-ff)*sThe Attempt at a Solution W=...

Hey! :o I want to calculate $\iint_{\Sigma}(x^2+y^2)zdA$ on the part of the plane with equation $z=4+x+y$ that is inside the cylinder with equation $x^2+y^2=4$. We can define the surface $\Sigma : D\rightarrow \mathbb{R}^3$ with $\Sigma (x,y)=(x,y,4+x+y)$, where $D$ is the space that is...

Homework Statement Two blocks slide on an incline of angle \theta . Block 1 has mass m1 and coefficient of kinetic friction μ1 with the surface, block 2 has mass m2 and coefficient of kinetic friction μ2. The gravitational acceleration is g. In terms of these parameters, under what condition...

Homework Statement The xy-plane serves as the interface between two different media. Medium 1 (z < 0) is filled with a material whose µr=6, and medium 2 (z > 0) is filled with a material whose µr=4. If the interface carries a current (1/µ0)ˆy (y- hat) mA/m, and B2 = 5ˆx (x-hat) + 8ˆz (z-hat)...

Hello , This is a question related to an everyday activity . My thinking - The base of the inclined plane is along the x-axis and it makes an angle θ with positive x-axis .We are looking from the +z axis . There will be three forces acting on the person . Weight , normal(perpendicular to the...

Hello, This is a bit more complex than my previous post, but I don't think it qualifies for university level difficulty. Please move this to the appropriate forum if my assessment is not correct. I have 4 vectors in three space where each vector has its tail at the same point (point B). id...

Homework Statement The picture below. Homework Equations cos2x=1-2sinx sin2x= 2sinxcosxThe Attempt at a Solution I got the modulus by using the Pythagoras theorem which is 2sin theta But I faced difficulty to find the argument. I have no idea why i end up with tan a (alpha) = cot theta which...

Homework Statement Is the gradient of a plane, the normal to the plane? If so, why? Homework Equations No idea, just a question that popped up in my head eon of plane: n(x-x1)+n(y-y1)+n(z-z1) The Attempt at a Solution I found the partial derivative of each, and got the normal.[/B]

Homework Statement Calculate the braking distance for a car traveling at a speed of 35.0m/s down a hill at an angle of 10.0 degrees relative to the horizontal. Homework Equations F=ma v=u + 2as[/B] The Attempt at a Solution The teacher briefly explained this in class saying that the total...

Homework Statement Why is that we can set two variables zero in an equation of a plane to find a point on that plane? What is the proof for this? Homework EquationsThe Attempt at a Solution

1. A plane is flying at 80m/s [n] in level flight. Draw a freebody diagram and state whether forces are balanced or unbalanced. -i wasn't sure what to draw :/

Homework Statement Suppose you needed to push a 1,500-N sofa up a frictionless ramp with a 30° angle. How much force would you have to apply to the sofa? Homework Equations f=ma The Attempt at a Solution I know that to find force you need to use the equation f=ma but I am not sure how I...

Homework Statement There is a mass on incline surface that is acted by foces. μ=0.8 m=2 kg θ=30° g=10 m/s^2 ##F_N##= normal force ##F_F##= friction force ##Fg_x## = horizontal gravitational component ##Fg_y## = vertical gravitational component Homework Equations ##F_N=mg~cosθ##...

Homework Statement Find th distance of point P to the plane OQR, O being the origin. "PS" is perpendicular to plane "OQR" P(3,-2,-1) S(x,y,z) O(0,0,0) Q(1,3,4) R(2,1,-2) Homework Equations A) The equation in terms of (x,y,z) obtain by triple product of OS,OQ & OR. OS.(OQXOR)=0... [all being...

I have a circle with centre (-4,0) and radius 1. I need to draw the image of this object under the following mappings: a) w=e^(ipi)z b) w = 2z c) w = 2e^(ipi)z d) w = z + 2 + 2i I have managed to complete the question for a square and a rectangle as the points are easy to map as they are...

Homework Statement Two objects of 2.8kg and 4.2kg are connected by an inextensible cord. The object's at rest on a plane inclined 22°, determine the object's acceleration and tension in the cord if a 60N force is used to push the object downward. Homework Equations ΣFnet = ma the plane is...

Sorry if this has been answered already, i searched for a while. I know how to solve the problem of the potential of a point charge near a grounded infinite conducting plane, and a line charge near an infinite conducting plane. If the plane isn't necessarily grounded, say its at some potential...