Planes Definition and 543 Threads

"Find the points on the surface 4x^2+5y^2+5z^2=1 at which the tangent plane is parallel to the plane 4x-37-1z=-2" Im very lost when it comes to this problem. I know that if the planes are parallel, the normal vectors will be parallel. So I think I need to multiply plane (4x-37-1z=-2)'s...

Consider two infinite parallel planes of charge, one in the yz plane and the other at distance x = a. (a) Find the potential everywhere in space when V = 0 at x = 0 if the planes carry equal positive charge densities + σ. (b) Repeat the problem with charge densities equal and opposite, and the...

Hello, I am a little confused on how to prove these half planes are convex, and my book does not actually show an example. ---------- So here is a problem, my book briefly talks about it: Show that the plane 2x - 3y >= 6 is convex. So if we let A = (2,-3), and X = (x,y), then we can write...

there are two planes: 3x+y+z=1 3x+z=0 find a vector U with positive first coordinate that is parallel to both planes. the way I went about solving this: the normal vectors are: <3,1,1> and <3,0,1>, the cross product of the vectors will give a vector perpendicular to the normal, which...

Have a question from materials science class: Using appropriate sketches determine the direction of the intersection of the following planes: (110) and (101) do I need to actually draw out these planes, then find 2 vectors for each. take the cross product, then use the lines perpindicular...

Hello. I need some help with the following problem: Find the component of u if u is perpendicular to the plane x- 3y + 4z =0 and the magnitude of u is 3. My work: Some vector v is on the plane v = 1i – 3j + 4k so then the dot product of u and v = 0 Now I’m stuck and don’t...

Consider the Earth's orbit around the sun to be in a plane A and the moon's orbit around the Earth to be in a plane B. How do these planes intersect? Are they parallel or perpendicular? At what angle do they intersect themselves? Does the angle stay the same, or does it vary.

What's the easiest way to make up two equations of a plane that intersect at a line?

hi all I am struggling to on these types of questions ill post here 1. find the equation of the plane containing the points A(-1,2,1) B(0,2,3) and C(4,-1,2) i tried to plot this on a x,y,z and maybe i rearranged to get formula n=CA * CB but its wrong heh no idea how to do this anyone can...

Just when I thought I understood the concept of planes and miller indices, I got stuck on a 'test your understanding' Q in my book. I can't understand that there can be two or more (110) planes in a crystal lattice? I thought there can be only one such plane. The question asks me to find the...

Two planes fly from Toronto to Philadelphia (To. - Philly). Plane A flies via Pittsburgh whereas passengers on plane B have a direct flight. Pitts. is 350km due south of To. and 390km due West of Philly. The airspeed of both planes is 400km/h and a steady wind is blowing from the east at...

Consider the line which passes through the point P(-3, -4, 3), and which is parallel to the line x=1+6t, y=2+4t,z=3+1t Find the point of intersection of this new line with each of the coordinate planes: xy-plane:(_,_,_) yz-plane:(_,_,_) yz-plane:(_,_,_) to find xy-plane, I am...

Hello, can anyone help me with this problem? Find an equation of the plane through P (3,3,1) that is perpendicular to the planes x +y = 2z and 2x +z =10 Thanks

Hi, first poster here. I'm stuck on a question in first-year University Maths. I'll put down what I know where I've done it. Question: Consider these linear equations: x + 2y - z = 2 2x + y + 3z = 5 x + 5y - 6z = 1 for the planes P1, P2 and P3 respectively. (a) Using Gaussian...

Well, I'm doing homework (again). I was introduced to homogeneous systems of planes and then asked why there must be at least 1 intersection point. The book gives very little (one sentence) on homogeneous systems so I tried to search around online. My guess is that since all of the...

I have been working on these two problems for a while now and I can't seem to come up with the right procedure to take them on: 1) Find the plane through the origin and parallel to the plane 2x - y + 3z = 1 * I thought this could be solved by taking the vector of the parallel plane...

Hi, Sometimes when a jet plane is flying above you you can see the white tail from the motors, and sometimes not. What is the reason for this? Why isn´t this visible all the time? regards t.

Hi, I suppose my question has to do with planes in general, rather than just tangent planes. Say you have a plane given by the equation z=\frac{\partial f}{\partial x}(x)+\frac{\partial f}{\partial y}(y). How would you find the equation of the plane perpendicular to this one? Thanks...

Hello I'm a grade 12 math student at WCI and I need some help with planes. As I understand it planes are 2D sections of grid. 2D sections of grid can't exist in real space because they have no thickness. How can anyone need to use something that has no thickness, why can we ever imagine it.

How do I find the line of intersection of two planes? I have an idea, but both of the planes have a -2z ie. Plane 1: 10x-4y-2z=4 Plane 2: 14x+7y-2z If I set them both equal to each other, I lose the z part. So, is there some other way to solve this, or am I missing something? Thanks!

please delete. please delete this thread.

Please help. Given the 3 vectors a = -21 + 3j - k, b = 41 - j + 2k and c = -3i + 2j - 3k: 1. Find the unit vector perpendicular to a and b + c. 2. Evaluate a . b x c I'm completely clueless on how to approach the first question. Any help would be great. I'm not sure which product...

Is there a point on the surface of x^2-3y^2+2z=4 where the tangent plane is parallel to the plane 2x+y-z=4? I can find a plane tangent to the surface at a certain point, but I'm lost on this one. Any help will be appretiated.

Hello, could someone please give me some help with the following question? Q. Determine all planes (in R³) orthogonal to the vector (1,1,1). This is how I started off but I am not really sure how I need to go about solving this problem. I begin(by somewhat assuming that the vector (1,1,1)...

I need to find the equation of a plane that is parallel to the plane 2x + 4y + 8z = 17 and contains the line { x = 3 +2t , y=t , z=8-t } . Not quite sure how or where to begin. Something having to do with a perpendicular vector maybe? Also, in a different problem, I need to find the...

How would you go about finding cartesian equations of intersecting planes when you have the vector equation of the line they intersect at. THere in obviously an infinate number of solution. The catch is that all the x,y,z values of the planes normals must not be 0. So I was thinking you but the...

The homework problem is confusing me a little bit especially b and c. I have attached the picture of the incline plane and object. Based on figure #1, assume the block is sliding down the inclined plane and that there is kinetic friction associated with the block and plane. Label all...

Hey guys thanks for the help on the last problem, I just had one more that I was trying to get finished studying for this big exam coming up: A block with mass m = 13.0 kg slides down an inclined plane of slope angle 32.8 ° with a constant velocity. It is then projected up the same plane...

Just before world war 2 there were many big planes and tanks that had lots of guns but were slow. People were trying to make the equivalent of battleships which had lots of guns and armor and were often faster than than smaller ships. however large planes and tanks were impractical. Why?

I am very confused regarding a few problems in Calculus III. Any help or hints to any of these would be greatly appreciated! 1.) Are lines L1 and L2 parallel? L1: (x-7)/6 = (y+5)/4 = -(z-9)/8; L2: -(x-11)/9 = -(y-7)/6 = (z-13)/12; The answer says that they are parallel, which I...

Hi, I got a few questions on ground effect : 1. When a plane lands, there is a period of ground effect, when the plane is less than 10 feet above the ground and the flight is very smooth. Can someone remind me why it is so smooth? 2. Does ground effect have any effect on regular or race...

This is my post that I posted in the calculus discussion area, but I know that there are a few people here in the same class (and using the same book!) so it's probably beneficial to post it here too. edit: go me! of course I forget to post the link lol...

This is in my multivariable course. How would I find the equation of the line where two planes meet? I worked out how to find the equation of a plane perpendicular to that line going through a point, Z, (in two planes, Ax + By + Cz +D = 0 and Ex + Fy + Gz + H = 0, take the cross product of...

Can anyone help me with parts (b) and (c) of this question: http://203.219.144.182/carl/q1ii.gif I've done parts (i) and (ii) but can anyone help with parts (iii) and (iv) http://203.219.144.182/carl/q2.gif answers for parts (i) and (ii): http://203.219.144.182/carl/q2a.jpg...

Planes and Bees Hey everyone...thanks ahead of time. This is a somehwhat general question. A person concluded that a bumble bee could not fly, and his basis was that he determined that a plane with the same design and wingspan proportions etc. could not fly. Now, of course this is wrong...

Inclined Planes and Acceleration Hi, I'm new to this forum and basically to physics itself, as I have previously concentrated my attention on the mathematical areas of calculus and algebra. I'm currently a sophomore at an Australian Catholic high school and have been recently tasked with a...

Physics Overview How would I exactly gain a basic understanding of all the basic physics topics and concepts? What materials could I use to increase my knowledge?

How can I show that 2 lines lie in the same plane? How can I get the equation of that plane? Thanks!

Could anyone help me summarize or if anyone knows good tricks in solving problems of lines intersecting with planes, etc, in 2d or 3d, the concept is same, but just want others opinion on what its basic idea is. i am able to do problems but i don't really understand them, i have to go back in my...

I need some help on this question... \rightharpoonup{r} = (0,0,5) + s(4,1,0) + t(2,0,2) which intersects the xz-coordinate plane in what line?

What is the mechanical reason why hurricanes are explored with propeller planes, and not jet planes? Is it because of the density of water in clouds therein?

i recently asked how airplanes work and i was give this answer: as velocity increases pressure decreases and the shape of the wing makes it so that the wind travels over the top of the wing faster than the bottom of the wing. so since there's a faster velocity on the top there is a lesser...

I read in an old metal working book that when a auto body panel is struck sharply with a hammer that for a microsecond or nanosecond there is a vibration or "shock waves" that allows the grains of metal to slip past one another and re-arrange slight. I am desperately looking for an explanation...