Planes Definition and 543 Threads

Hiya, I have a question in high school math, vectors to be precise: The point K(3.5,-0.5,-2) is the intersection point of the plane S1: mx-7my+5z+3=0 with the line l1: (n,1,-2)+t(-1,1,0) a) find the parameters n and m b) find the equation of the plane that contains the line l1 and is...

Hi everyone, I really would like to know the whole background with physics dealing with how planes work, and if making a Styrofoam plane is the same idea with physics but just slightly different. I am a college student majoring in physics and trying to start a company somewhat dealing with...

∴1. Homework Statement Find an equation for the plane that contains the point (1,-1,2) and the line x=t, y=t+1, z=-3+2t? 2. Homework Equations The Attempt at a Solution I don't know what I am doing wrong but everytime I try to do these plane questions my amswer is always the opposite sign of...

I have a couple of questions that i thougth this group could help me with. 1. A plane (SR71) takes off from the equator, with a lateral speed, relative to space of 1000mph. (earth rotational speed) say it takes an hour to get there so, its going 10,000mph or something. . Tt flys over the...

Prove that the paraboloids: \frac{x^2}{a_1^2}+\frac{y^2}{b_1^2}=\frac{2z}{c_1}; \frac{x^2}{a_2^2}+\frac{y^2}{b_2^2}=\frac{2z}{c_2}; \frac{x^2}{a_3^2}+\frac{y^2}{b_3^2}=\frac{2z}{c_3} Have a common tangent plane if: \begin{bmatrix}a_1^2 & a_2^2 & a_3^2\\ b_1^2 & b_2^2 & b_3^2\\ c_1 & c_2 &...

Hi, I am having trouble understanding why three vectors that lie in the same plane can't form a tetrahedron. If the plane is somewhat vertical or titlted will it not be possible for one vector to higher up than another so that you have a difference in height? Also, for three vectors to form a...

Homework Statement Find unit vector(s) that are parallel to both of the planes 6x + y + z = 1 and x − y − z = 0 . Homework Equations N/A The Attempt at a Solution OK. So here is my reasoning - I find the normal of both the given planes and find the cross product between the vectors. The...

Homework Statement ** sorry, answer in the book doesn't make sense ** A british concord and a French concord flew in opposite directions around the world, a distance of 40K km. The BC covered half its distance at 2500 km/h, and the other half at 1000km/h. The FC spent half its flight time at...

$\tiny{s4.854.13.5.47}$ $\textsf{a. Find symmeteric equations for the line of intersection of planes}\\$ $\textsf{b. Find the angle between the planes}\\$ \begin{align}\displaystyle j+y-z&=2 \\ 3x-4y+5z &=6 \end{align} \begin{align}\displaystyle n_1&=\langle 1,1,-1\rangle\\ n_2&=\langle...

$\tiny{{s4}.{13}.{5}.{41}}$ $\textsf{find if planes are $\parallel, \perp$ or $\angle$ of intersection }\\$ \begin{align} \displaystyle {P_1}&={x+z=1}\\ \therefore n_1&=\langle 1,0,1 \rangle\\ \\ {P_2}&={y+z=1}\\ \therefore n_2&=\langle 0,1,1 \rangle\\ \\ \cos(\theta)&= \frac{n_1\cdot...

Homework Statement [/B] For part b , i think one of the angle either $$\theta_s$$ or $$\theta_p$$ is wrong For the second question , what is plane stress ? Homework EquationsThe Attempt at a Solution [/B] 1.) Because in mohr's circle, the maximum shear stress on the vertical axis , for the...

Homework Statement Let S be a sphere with the equation ##(x-2)^2+y^2+z^2=2 ## and let p a line which satisfies the condition ## p \in (\Pi \cap \Sigma) ## where ##\Pi## and ##\Sigma## are planes with equations: ##\Pi :x+z=2## ##\Sigma: 5x-2z=3## a) Show that S and p have exactly one common...

Homework Statement Find the surface area of portion of plane x + y + z = 3 that lies above the disc (x^2) + (y^2) < 2 in the first octant ... Homework EquationsThe Attempt at a Solution Here's the solution provided by the author ... I think it's wrong ... I think it should be the green...

Homework Statement Find the volume of solid which is bounded by z = 4-x-y and below by region in the plane of 0<x<2 , 0<y<1 When i use zx -plane projection , i found that my ans is different with the ans of using xy projection ...Which part i did wrongly ? From the ans given , volume = 5...

Homework Statement Given two planes, P1, P2. Find parametric equations for the line of intersection between the two planes. Homework Equations P1 = 2x -3y + 4z = 3 P2 = x + 4y - 2z = 7 The Attempt at a Solution Let N1 be the normal vector to P1, and N2 be the normal vector to P2. Then, N1...

Homework Statement [/B] Calculate the volume bounded by the plane/cylinder x^2+y^2=1 and the planes x+z=1 and y-z=-1. Homework Equations / The attempt at a solution[/B] It is pretty basic triple integral in cylindrical coordinates. For some reason, I can't get the right answer. I'm using...

Homework Statement A uniform current sheet in free space is given to be, in phasor form, \vec{J}=\vec{x}J_0e^{-jk_1y} located at the z=0 plane. k_1 < k_0 where k_0 is the wavenumber in free space. a) Describe qualitatively the characteristics of the wave generated by the given current source...

What is the angle of intersection between the two planes in ℝ3 with general equations x-y=5 and y-z=7? I know that the angle between then is equal to cos-1 (u⋅v/||u|| ||v||) but I am stuck on the general equations given, how can I solve when given these ?

I had no idea this technology existed, and was so effective. Very nice! Lots of documented saves over the past few years... http://www.cnn.com/videos/us/2016/03/08/new-york-parachute-plane-crash-orig-vstan.cnn :smile:

Homework Statement Homework Equations Conservation of Energy / Virtual Work $$\sum_i m_i g h_i = 0$$ The Attempt at a Solution Moving the pulley I labeled A down by ##\delta y## moves ##w## down by ##\delta y##, and moves ##W## up by ##\frac{1}{2} sin\theta##. So by conservation of energy...

I am struggling to obtain the hkl planes of a kikuchi pattern. The material is Aluminum with a = 4.05 A. There are 4 bands, the first, b1, is pointing vertically down, the second, b1, is at the 34.5 degree angle from b1, the third, b3, is 65 degrees from b1, and the fourth, b4 is 90 degrees from...

Homework Statement a) Find the acute angle between the line ## r = i+3j+5k+t (2i+4j+k) ## and the plane x-y+z=0 b)Two planes are defined by the equations ## x+2y+z=4## and ## 2x-3y=6 ## i. find the acute angle between them. ii. find a vector equation of their line of...

Homework Statement Find the equation of all planes containing the points P(2, -1, 1) and Q(1, 0, 0) Homework EquationsThe Attempt at a Solution I use PQ to get a vector, (-1, -1, 1). I some how need to use another vector so I can use the cross product to find the planes. So i let another...

Pourquoi une onde plane n'a pas de réalité physique

How can I find the line of intersection between the planes 2x-y+2x+1=0 and -4x+2y-4x-2=0 I realize these are parallel as they are multiples of each other, but I'm not sure how to solve for the point. I also have to convert this line into parametric, cartesian and vector form. Sorry for the...

Stuck on the last 3 systems on my worksheet, if someone could give me more than just the answer but also teach me how, it would be much appreciated! "Determine the nature of the intersection if it exists) between the following sets of planes. If it is a line, find the equation of it. If it is a...

I've done a question similar to this, however this one has no complete equations i can solve for. Determine the equation of the plane that passes through (1,3,8) and is perpendicular to the line of intersection of the planes 3x−2z+1=0 and 4x+3y+7=0. I know to take the cross product of the two...

Homework Statement Find parametric equation of the line through the point ##(4,0,-4)## that is parallel to the planes ##x-8y+7z=0## and ##4x+3y-z+4=0##. Homework Equations ## \vec r = \vec r_0 + t\vec v ## (for orthogonal vectors) ## v \bullet w = 0 ##[/B] The Attempt at a Solution So I...

This question is slightly related to my other plane, but I didn't want to post in the same thread as I didn't want the other one to get derailed. If I have blueprints for an RC plane, and I scale down everything by a ratio (let's say 1/2), would it still work just as well? Or would it follow...

Homework Statement The plane with surface charge sigma lies in x-z plane at y=0, parallel to it at y=a there is a grounded plane. What is the field just above the bottom plane, find the potential between the planes Homework Equations discontinuity E=sigma/epsilon, V=Qd/Aepsilon take the...

Hello everyone, I have this problem at which I don't understand the solution. So we have an inclined plane and a block of mass m standig on it , at it's highest point. Knowing the angle of the inclined plane(alpha) , the height of the inclined plane, the friction coefficient between the 2...

Homework Statement X'=x-y^2 Y'=x^2 -xy -2xHomework Equations Find the critical point of this system. The Attempt at a Solution I know one point is (0,0). When I tried it I got sqrt(x)= 2 and sqrt(x)= 1 but the point (1,1) doesn't fit later parts of the question. I'm also aware that since a...

Hello every one. It's obvious that all of the major planetary objects in our solar system orbit the sun in roughly the same plane. My question is, is our solar system in a similar plane as it orbits the center of the Milky Way? If so, do most star systems share the same plane? This came to mind...

Homework Statement Find an equation of the line where the planes Q and R intersect. Q: -2x + 3y - z = 1; R: x + y + z = 0 Homework Equations Equation of a Plane: ax + by + cz = d, where \vec{n} = <a, b, c> Equation of a Line in R^{3}: \vec{r}(t)=<x_{0}, y_{0}, z_{0}> + t<x,y,z> The Attempt at...

Hello everyone I am trying to design a ramjet engine. For that I need measurements of its parts. Does anyone know how to calculate them or have a link to a website where I could find more information?

Homework Statement the volume density of a body centered cubic lattice is 5.3*10^22 Calculate the lattice constant, effective radius of atom, surface density on 110 plane, and distance between two nearest parallel 110 planes. Homework Equations 4/a^3= volume density 2/sqrt2*a^2 The Attempt at...

Homework Statement Two planes are given by the equations x + y + z = 1 for the plane P1 and x − y + z = 1 for the plane P2. (or) P1 : x + y + z = 1 P2 : x - y + z = 1 Q. The Question Find the coordinates of a point of intersection of the planes P1 and P2 Homework...

This problem was on my exam last week, and I've been having some troubles coming up with a solution. 1. Homework Statement Two semi-infinite conducting planes are connected by insulating glue, they make a 30º angle with each other. One of them is at ground potential, and the other one at V0...

Homework Statement [/B] Find the cross product equation for the line L that forms the intersection of the planes: A: 2x - y + 2z = 1 and B: x + y - 2z = 1. Homework Equations General equations for planes A and B: (a, b, and r are vectors). A: a dot r = 1 B: b dot r = 1 r = xi + yj + zk ...

Hello, I am stuck between two majors to study in college, Computer Engineering and Aerospace Engineering. About me: I am going to be a senior next year and I am going to be taking high level ap calculus and ap physics. I am a very creative person and am very good at the arts and industrial...

Hello,Suppose I have a vector equation: \begin{cases} x=0+10t\\ y=0+10t\\ z=0+10t \end{cases} Which forms the symmetric equation \frac{x-0}{10}=\frac{y-0}{10}=\frac{z-0}{10} Now, I know the symmetric equations can be split up so that you can form the two planes whose intersection yields the...

My source is Walter A. Harrison:"Applied Quantum Mechanics" Section 5.4 p.83. When studying diatomic molecules such as N_2 one may make use of the high symmetry of the molecule with relfection planes σx,y,z. In Harrison it is said that each molecular orbital can be chosen to be even or odd under...

"Two planes leave a city for another city that us 600 miles away. One of the planes is flying 50 miles per hour faster than the other. The slower plane takes 2 hours longer to reach the city. What is the rate of each plane? Write and solve a system of equations." My daughter is well aware that...

I wondered about possibility of using ground effect by blended wing body, turboprop planes. Purposes: -to save fuel (for example for flying tankers); -to return partially damaged plane; -to hide under radar and become visible for ships in the last moment; -to allow flight of overloaded plane...

Homework Statement Let W be the intersection of the two planes: x-y+z=0 and x+y+z=0 Find a basis for and the dimension of the orthogonal complement, W⊥ Homework EquationsThe Attempt at a Solution The line x+z=0 intersects the plane, which is parameterized as t(1, 0, -1) Then W⊥ is the plane...

Hi All, Question: Consider the tetrahedron, T, bounded by planes x=2, y=0, z=0 and 3x-6y-2z=0. Determine the integral \iiintyDV which is the y coordinate of the centre of mass. I am getting a negative area which leads me to believe I'm doing something wrong. Working is attached. Help would...

Homework Statement (I did not copy the problem statement, but basically solve the system of equations if there is solution and give a geometrical interpretation) P1: 2x - y + 6z = 7 P2: 3x + 4y + 3z = -8 P3: x - 2y - 4z = 9 Homework Equations Scalar triple product: n1⋅(n2 × n3) The Attempt...

I understand the intuition behind it, but I'm unable to prove it. Essentially, three non-colinear points define a plane, and so by adding one more point on the plane, it becomes dependent. This means that the determinant is 0, since there is probably a dependent row lying around. Also, how is...

Hey all, for some software I'm writing a sub problem of a bigger math problem I have is that I need to find the line of intersection of two planes, One can obtain the normal via the cross product but I am stuck at how to find a point on that line as they're seems to be too many variables...

Homework Statement Two boxes of equal mass m are connected by a light string over a massless pulley, and rest on surfaces of inclination θ and φ, θ>φ. The boxes are released from rest. The coefficient of kinetic friction between the boxes and the surfaces is μ. Determine the magnitude of the...