Planes Definition and 523 Threads

Homework Statement Find parametric equations for the line of intersection of the planes x + y + z = 1 and r = (1, 0, 0) + \lambda(2, 1, 0) + \mu(0, 1, 1) where \lambda, \mu \in R Homework Equations The Attempt at a Solution I attempted to convert the 2nd plane equation to scalar form by...

Homework Statement The planes ∏1 and ∏2 have equations 3x - y - z = 2 and x + 5y + z = 14 respectively. Show that the point (3,1,6) lies on both planes. The Question: By finding the coordinates of another point lying in both planes, or otherwise, show that the line of intersection of ∏1...

Homework Statement Find symmetric equations for the line of intersection of the planes The planes: 5x - 2y - 2z = 1 4x + y + z = 6 Homework Equations r = r0 + tv x = x0 + at y = y0 + bt z = z0 + ct The Attempt at a Solution I have attempted this in many different manners and would like...

Homework Statement Find the volume of the region bounded by the cylinder x^2 + y^2 =4 and the planes z=0, and x+z=3. Homework Equations V = ∫∫∫dzdxdy V=∫∫∫rdrdθ The Attempt at a Solution Alright, so I feel as though I'm missing a step somewhere along the way, but here's what I've gotten...

Homework Statement Line of intersection between P1: x+y+z=7 and P2:2x-3y-z=-8 crosses the XZ plane at point A and crosses the YZ plane at point B Find the length Of AB Okay so first of all i`m having trouble with understanding crossing the `XZ`plane or `YZ`plane. does this mean that...

Homework Statement The three lines intersect in the point (1; 1; 1): (1 - t; 1 + 2*t; 1 + t), (u; 2*u - 1; 3*u - 2), and (v - 1; 2*v - 3; 3 - v). How can I find three planes which also intersect in the point (1; 1; 1) such that each plane contains one and only one of the three lines?Homework...

And vehicles on the ground as well, in particular heavy ones like trucks. How do the ground and windows to vibrate?

NEED CORRECTION, also this . means dot multiplication. My teacher comments: #6) you've made some errors (-2 marks) #8) correct, they intersect at a point, but you need to find the point like you did in #7 for full marks (-3 marks) 6.Determine the intersection, if any, of the planes...

Homework Statement Find cartesian equations of the line of intersection of the planes x+3y-6z =2 and 2x+7y-3z=7 The Attempt at a Solution What I did first was I cross product the 2 equation and then I got 33i-9j+k Then I took both of the equation and let y = 0. After that my answer seems...

First time poster, but have always had conversations physics related with friends, none that are experts lol. I'm also a fan of movie and the physics/realism within films. Recently I've been listening to Neil D. Tyson's startalk podcast about the science in movies (his story on the error of the...

Homework Statement Consider z = -3x - y + 11 Find a unit vector perpendicular to the plane, and find a vector parallel to the plane. Homework Equations The Attempt at a Solution 1.) 0 = -3x - y + 11 - z -11 = - 3x - y - z Perpendicular vector is then: -3i -j -k...

(a) Find the equation of the plane p which passes through the three points (A 1,0,1), B(2,−1,1) .and C(0,3,2) . (b) Find a scalar parametric form of the equation for the line which passes through the point D(−1,1,1) and which is perpendicular to the plane p. (c) Let E be the point where...

For positive a and h, let A designate the region of R3 enclosed by the elliptic hyperboloid, x2 +y2 -z2 =a2 and the two planes, z= -h/2 and z=h/2. Determine the volume of A So I figure this will be a triple integral in cylindrical coordinates. the first integrand being from -h/2 to h/2...

I have been using the formula a = g sin(theta) to process my data I am however pretty sure something is wrong. I doubt it is my data that is wrong, even though when I look at them they look weird in the sense that I would think that after one second the acceleration should have been doubled...

Homework Statement The Question Says: Given tow lines and a plane: The First Line is:L_1:(x y z):= (-4 3 4)*t +(7 2 -1) The Second Line:L_2:(x y z):=( -3 5 5)*s +(-1 62 -11) The Plane is :P:(x y z)dotted with(9 -2 3)=-4 (A)At which point do L_1 and P intersect? Check if this point lies in...

1. Evaluate the integral ∫VxdV inside domain V, where V is bounded by the planes x=0, y=x, z=0, and the surface x2+y2+z2=1 Answer given: 1/8 - √2/16 (which is NOT what I got.. ) 2. The attempt at a solution Ok, it's a triple integral, I know this. ∫dx runs from 0 to 1 ∫dy...

Homework Statement A sphere of radius R with centre at the origin is cut by two parallel planes at z=\pm a, where a<R. Write, in cylindrical coordinates, a triple integral which gives the volume of that part of the sphere between the two planes. Evaluate the volume by first performing the r,θ...

Homework Statement Find the volume of the solid bounded by the parabolic cylinder y = x^2 and the planes z = 3-y and z = 0Homework Equations The Attempt at a Solution Obviously, a triple integral must be used in the situation. Our professor never explained how to find the limits of...

I'm trying to learn crystallography and I've had trouble with this concept since the very beginning of the course. It's been so long since it's been introduced that I'd be embarrassed to ask the prof. Right now, I seem to understand the principles of diffraction based on the Miller model; that...

Homework Statement Find the volume of the region bounded by the planes 7x + 6y + 8z = 9, y = x, x = 0, z = 0. Homework Equations Multiple integration. The Attempt at a Solution My attempt at a solution is attached. To test, I computed the answer with Wolfram Alpha which yielded an...

If I have a cylinder with a radius r and an axis that passes through point b with the direction of vector n, show that its equation can be written in any of the following forms: 1) |(p-b) X n| = r 2) (p - b) X n = r.e (where e s ia unit vector orthogonal to n) 3) |(p-b) - ((p-b).n).n| = r...

I've watched a lot of youtube videos on how planes fly and they all gloss over one detail that I can't understand. They say that the foil is shaped such that the air on top must travel faster than the air on the bottom. By Bernouille's equation, this creates higher pressure on the bottom than...

In jet aircrafts where are the alternators, how are they connected to the jet engines? Is it using belts? Are they on the wings? Thank you Regards

I do not understnad how x+y+z=0 can be a plane, I thought a plane has 2 dimensions, this is all :) thanks.

Here is what I've done so far How do I draw the Phase portrait for this system? Have I done everything correct so far? Thanks

Homework Statement given the planes with equations: x + y + 7z = -7 2x + 3y + 17z = -16 x + 2y + (a^2 + 1) z = 3a find values for the constant a for which: -there are no solutions -the planes meet in a line. in this case find the parametric equation of the line -meet at a point. then find the...

Homework Statement The equations sin(xyz) = 0 and x + xy + z^3 = 0 define planes in R^3. Find the osculating plane and the curvature of the intersection of the curves at (1, 0, -1)Homework Equations Osculating plane of a curve = {f + s*f' + t*f'' : s, r are reals} Curvature = ||T'|| where T is...

This is a question that has been burning for some time, I have been wondering, instead of plotting the different points of a function onto a steady x and y axis, is it possible to have a single point (at the origin) and have the planes move instead. The space moving around the point. When I...

Homework Statement Find the point of intersection of the lines r(t)=< 2t+1, 3t+2, 4t+3> and x=s+2 y=2s+4 z=-4s-1 Then, find the plane determined by these lines. Homework Equations Intersection is when points meet. So, just equating x,y, and z variables will yield the point of...

Homework Statement A block of ice of mass m slides down an incline that makes an angle θ = 40.7° with the horizontal. In trial 1 there is no friction; the block starts at rest and takes time t to reach the bottom of the incline. In trial 2 there is friction, and the the block slides down the...

Homework Statement My problem is one pertaining to my Vector Calculus course. The assignment is asking us to "Find equations for the planes tangent to z = x2 + 6x + y3 that are parallel to the plane 4x − 12y + z = 7." The problem I'm having with the problem is the plural aspect. It states...

Homework Statement Im working currently with vectors. The question asks for the distance between two planes given by the two following equations: x + y -2z = 0 3x + 3y -6z = 1 Homework Equations I know the planes, H1, and H2 are parallel, so I can pick any random point on either...

Homework Statement Find the parametric equations through point (5,-1,3) parallel to the line of intersection between 2x-y+z=1 and 6x-y-z=3, where 0≤t≤1 Homework Equations 1. Find normal vectors for both planes 2. Take cross product of both normal planes ... The Attempt at a...

How do you find the distance between two parallel planes? My book gives me only a formula and doesn't say how they got it

Homework Statement do you notice a relationship between the plane and directions of the same miller index? what is it? Homework Equations I've done planes and directions (111), [111], (112), and [112] The Attempt at a Solution I believe the direction is normal to the plane on first...

Homework Statement Find parametric equations for the line which passes through the point (1; 2; 3) and is parallel to both of the planes 3x + y + 5z = 4 and z = 1 -2x. I have seen the result for this problem, but it's different than mine. I'm not sure, what I'm doing wrong. Please, help...

I'm trying to plot something like x+y=2 in 3D. The image should look like this: Been trying to do it in Mathematica using Plot3D, but the it treats the input as a function of z. Another example: Plot3D[x=4,{x,0,10},{y,0,10},AxesLabel{x,y,z}] plots z=4, not x=4. A similar thread, with no...

Please help me! Find angle between planes (011) and (001)?

how do i find the angle between the plane x=0 and the plane 2x+3y-z=4?

Homework Statement The plane that passes through the point (1, 6, 4) and contains the line x = 1 + 2t; y = 2 - 3t; z = 3 - t where t is an element of R Homework Equations x = 1 + 2t; y = 2 - 3t; z = 3 - t The Attempt at a Solution Let L be the solution. L = (1,6,4) - ? t = (x -1)/ 2 =...

Is it possible to find a directional derivative for a point on z = f(x,y) at a point (x,y) in a direction (u1,u2) using the plane tangent to z at (x,y)? If so, how? Thanks!

I recently had a discussion with a guy who believes that by putting a big slot in his PCB ground plane he will protect his analog domain from the noise originating in his digital domain. I don't agree with this view (hence the discussion), for various reasons, but to keep this post on point I...

Homework Statement find the point of intersection of the lines x=2t+1, y=3t+2, z=4t+3 and x=s+2, y=2s+4, z=-4s-1 then find the plane determined by these lines Homework Equations The Attempt at a Solution i have no idea how to find the point of intersection for those two lines...

Homework Statement S is the surface with equation z = x^2 +2xy+2ya) Find an equation for the tangent plane to S at the point (1,2,9). b) At what points on S, in any, does S have a horizontal tangent plane? The Attempt at a Solution F(x,y,z): z = x^2 +2xy+2y F_x = 2x + 2y F_y = 2x + 2...

Homework Statement ∫∫s x √(y2 + 4) where S: y2 + 4z = 16, and portion cut by planes x=0, x=1, z=0. Homework Equations I attempted to solve using the surface area integral formula, whereby this double integral is transformed to ∫∫f(x,y,g(x,y)) √((∂z/∂x)2 + (∂z/∂y)2 + 1) dA The...

The moon orbits the Earth on nearly the same plane as the Earth orbits the sun. Does this coincidence of orbital planes scale up? Do the planets in our solar system orbit on a plane that is parallel to the plane of the milky way? What about planets in other solar systems in the milky way?

Is it possible for two planes to meet in a point instead of in a line?

Homework Statement Suppose a mountain is described by the function z = 10x^2 * y − 5x^2 − 4y^2 − x^4 − 2y^4 and that you are standing at the point (1,1,−2). The positive x-axis points east and the positive y- axis points north. If you walk in the northeast direction what angle above the...

We are being asked to find the eq's for normal, osculating, and rectifying planes for the following equation: r(t) (cos t)i + (sin t)j - k @ t=pi/4 I have already found the following: T(pi/4) = (-√2/2)i + (√2/2)j = 0k N(pi/4) = (-√2/2)i + (-√2/2)j + 0k B = 0i + 0j + k But, I don't...

Homework Statement You have a pair of inclined planes such that a block that slides down one can slide up the other without losing any energy in the transition. The inclined planes are both at an angle θ from the horizontal, as shown in the diagram. The inclined plane on the left is...