Planes Definition and 523 Threads

Homework Statement Find the equation of a sphere of radius 3 which is tangent to both the planes x-2y+2z=3 and 3x+4z=8 Homework Equations The only eqn's I need are cross product and MAYBE the distance formula. The Attempt at a Solution Initially I shifted each normal vector by...

Homework Statement Given the following 2-dimensional plane in R^4 written in parametric form: x_1 = 1 + (-1)s x_2 = 0 + ( 1)s x_3 = 1 + (-1)t x_4 = 0 + ( 1)t a) find a 2-dimensional plane that does not intersect it b) find a 2-dimensional plane that intersects it to form a point c) find a...

Homework Statement let p1 and p2 be planes in R3, with respective equations: x+5y-z=20 and 2x+5y+2z=20 These planes are not parallel. Find the standard equation for the plane that is orthogonal to both of these planes and contains the origin. The Attempt at a Solution I have only managed to...

Homework Statement A student decides to move a box of books into her dormitory room by pulling on a rope attached to the box. She pulls with a force of 130.0 N at an angle of 15.0° above the horizontal. The box has a mass of 25.0 kg, and the coefficient of kinetic friction between box and...

Homework Statement Two airplanes taxi as they approach the terminal. Plane 1 taxies with a speed of 11 m/s due north. Plane 2 taxies with a speed of 8.5 m/s in a direction 20 degrees north of west. a) What is the magnitude of the velocity of plane 1 relative to plane 2? b) What is the...

Homework Statement Find two different planes whose intersection is the line x=-7+t, y=9-t, z=6+2t. Write equations for each plane in the form Ax+By+Cz=D.Homework Equations The solutions are x+y=2; 2y+z=24; but I do not know how to obtain these answers. (This is not for class work, I am just...

Homework Statement Find the shortest distance between the 2 planes: 2x+2y-z=1 and 4x+4y-2z=5 How do we approach this problem? I used the approach of finding the point at which the normal of one plane intersects the other plane and then determining the length of this vector. The...

Homework Statement r(t)={sin(pi*t),ln(t),((1/4)e^t} At what time(s) does the object intersect one of the coordinate axes? At what time(s) does the object intersect one of the coordinate planes? During what times t is the object in the first octant? Homework Equations Not...

Homework Statement The problem states to find an equation of the plane consisting of all points that are equidistant from (-1,3,-1) and (-2,-3,03) and having -1 as the coefficient of x. The Attempt at a Solution I actually got the solution by finding a vector using the two...

Homework Statement 1)show that the lines l1 and l2 intersect and find their point of intersection. l1: x+1=4t y-3=t z-1=0 L2: x+13=12t y-1=6t z-2=3t 2)The plane through the points p1(-2,1,4),p2(1,0,3) that is perpendicular to the plane 4x-y+3z=2 3)Find the distance between the given skew...

Homework Statement Find a plane perpendicular to the two planes, X+Y=3 and X+2y-z=4 I know i take the cross product of both so i get <1,1,0> and <1,2,-1> But when i do the cross product i get x-y+z book tells me x-y-z what am i doing wrong? Not sure why the z is negative. The...

Hi! I have already write everything on the pictures(In attachment), I have already circled the correct answer, however, I am not sure explain it correctly. So, can you check my explanation or question? Thanks!

Hi, All: This is a post from another site that was interesting but was not answered: can I reasonably > argue that three planes in 3-space are not likely > to intersect at a point using the fact that >t GL(3,R); > the subset of invertible 3x3-matrices has measure 0 > in...

Why can't Jet planes fly in space? Is is because it doesn't get lift or is it due to the absence of atmosphere?

Hi, just curious as to whether we can map any 2-planep: ax+by+cz=d into any other 2-plane p': a'x+b'y+c'z=d' by using a linear map (plus a translation , maybe). I was thinking that we could maybe first translate to the origin , for each plane, then , given the angles ( t,r,s) with...

For a homogeneous system of 3 equations in 3 unknowns (geometrically this is 3 planes in space all containing the origin) describe the relationship between the (three) geometric possibilities for the solution set and the number of free variables (non pivots) in RREF(A) where A is the...

Hello I am having a problem with the following question. Homework Statement Determine which statements are true in 3. (Select all that apply.) (a) Two lines parallel to a third line are parallel. (b) Two lines perpendicular to a third line are parallel. (c) Two planes parallel to a...

Homework Statement The plane P1 contains the points A,B,C, which have position vectors a=(0,0,0), b=(1,1,8) and c=(0,1,5) respectively. Plane P2 passes through A and is orthogonal to the line BC, whilst plane P3 passes through B an is orthogonal to the line AC. Find the coordinates of r, the...

I am having trouble understanding what exactly Bragg planes are physically. I understand how they behave, in that they act like mirrors and reflect matter waves, but what exactly is the wave bouncing off of? for instance I can guarantee any physics textbook always has a picture like...

Hello ! I have an exam this Wednesday... your help will be appreciated... There are two types of questions I can't figure out how to answer... the first is this one: Find the potential between two parallel planes. The first is in x=0, the second in x=L. \Phi(x=L)=\Phi_0 |sin(ky)| and...

Okay, I am currently reading about motion on inclined planes and how the normal force acts directly perpendicular to the surface of the plane and how the gravitational force, obviously, acts downwards. Since the two forces are not inflicted in opposing directions, we split the gravitational...

Lets say I have an inclined plane and I roll a solid cylinder down it and slide a brick down it. And let's say I slide the brick down on oil,Or better yet I slide a superconductor down and have It float above bar magnets. The superconductor moving down the plane will always beat the...

Homework Statement Find the equations for two spheres that are tangent to the plane x+y-z=3 and x+y+z=9 and the line x=t , y=2t, z=3t passes through its center. Preface: This problem was on a test I took yesterday. My professor handed it back today. The relevant equations and work are what...

Homework Statement If the left hand slope makes a 60 degree angle and the right hand slope makes a 20 degree angle. the left hand mass is 2.1 kg, and the right hand mass is unknown. what would the right hand mass be given a downward acceleration of .64 m/s^2. ? upslope at .76 m/s^2...

Homework Statement The normal vector of each of the following planes is determined from the coefficients of the x-, y-, z- terms. pi1: a1x+b1y + c1z + d1=0 pi2: a2x+b2y+c2z+d2=0 pi3: a3x+b3y+c3z+d3=0 Define the extended vector for each plan as follows: e1= [a1, b1, c1, d1] e2= [a2, b2, c2...

I posted this in "Materials & Chemical Engineering", but it seems a little more active here. I'm confused with trying to find the slip systems of a simple cubic. I understand the slip plane would be along the plane with the highest atomic density (a close packed plane). But I don't quite get...

Hello, I have a question regarding inertia. When we are on a plane, when it increases its speed we feel a force that goes on the opposite direction pushing us against the seat right? What about the air inside the plane, are there any difference in pressure due to inertia?

Homework Statement The following system of equations represents three planes that intersect in a line. 1. 2x+y+z=4 2. x-y+z=p 3. 4x+qy+z=2 Determine p and q 2. The attempt at a solution The problem I have with this question is that you are solving 5 variables with only 3 equations. I...

Homework Statement Find all the intersection points of the planes: 2x-y-z=3 x+2y+3z= 7 Homework Equations Whats the best n most simplest way to go about this question. Thanks The Attempt at a Solution

In this question: http://imageshack.us/m/705/917/questionn.png I know how to get the normal vector and the tangent plane but I have no idea how to get the equation for a line connecting the tangent plane to a x - y = 0 plane.

Calculate in parametric form and describe how the planes intersect Where: P1 = x-3y+5z=6 P2 = 2x-7y+9z=2 My attempt Put planes in matrix form: 1, -3, 5, 6 2, -7, 9, 2 Find Echelon Form 1, -3, 5, 6 0, -1, -1, -10 Z = free variable = a So: -y-z=-10 y = 10 -...

A sphere has two parallel tangent planes with equations x+2y-2z=37 and x+2y-2z=-11. One of the points of tangency is (-7,5,7). Find the center and radius of the sphere. I'm not really sure how to do this. I know that the point (-7,5,7) lies on the x+2y-2z=-11 plane. The distance from...

Homework Statement I am given two lines in vector form in 4-space. I need to write an equation for the plane that is parallel to one line, and contains the other line.Homework Equations well i know that in 3d I would find a normal vector for the plane that would be perpendicular to both lines...

Say there is are three hypothetical infinite parallel planes with charges on it. So let's imagine the three planes from left to right, or planes one, two and three. Plane-three is fixed to the reference frame. Plane-one and plane-two have a fixed separation distance between each other, but...

Homework Statement 4. The domain D is a tetrahedron bounded by the planes x = 0, y = 0, z = 0 and x + y + z = 1 Calculate (a) The volume of the domain. (b) The x-coordinate of the centre-of-mass of the domain, assuming constant density. (c) Find, in terms of x and y the vector R from the origin...

Vectors-planes and lines -------------------------------------------------------------------------------- 1. Homework Statement Two planes have equations 2x-y-3z=7 x+2y+2z=0 Find a vector equation for their line of intersection 3. The Attempt at a Solution I haven't learned...

Hi, all: Say we have a bare-bones Vector Space v, i.e., V has only the basic vector space layout; no inner-products, etc., over a finite field . I think then , we can still define a line in V as the set {fvo: vo in v, f in F}, i.e., as the set of all F-multiples of a fixed...

What, exactly,does spacing between three dimensional lattice planes mean?Does it refer to the formula d=2*pi/(translation vector)? *I am an engineering undergraduate and this word is in my syllabus in topic crystallography.I was wondering what it meant? Also, can someone tell me in...

The line of intersection of two perpendicular planes is r=(-1+5t)i +(5-t)j +(7-4t)k. One plane is 5x-3y+7z=29. Find the rectangular equation of the other plane. The Attempt at a Solution I think I need to find three points in the desired plane. (one point being (-1,5,7)?)

Homework Statement Determine value of k when thehse are perpendicular: [x,y,z] = [1+4s+kt, 2+2s+t, 7+2t] and [x,y,z] = [4,1,-1] + s[1,0,5] + t[0,-3,3] The Attempt at a Solution I learned that in 2 and 3D, two lines are perpendicular only if, after solving for the t in front of the...

Hello All, I need help in my Calc 3 class and I decided to come here for homework help. What I'm looking for is someone to just check my work for a couple of homework problems. I've already done the problems, I would just like my work checked. Anyone who helps, your kindness is greatly...

Homework Statement Find the volume of the solid bounded by the planes x = 0, y = 0, z = 0, and x + y + z = 9. Homework Equations . . . ? The Attempt at a Solution After drawing out the picture with z=0 I have a line going from 0,9 to 9,0 bounded by the x and y-axis giving me a triangle...

1. This is problem 2.10 from the book "Calculus of Several Variables by C.H Edwards": Let the mapping F: R2->R2 be defined by F(x1 , x2) = (sin(x1 - x2), cos(x1 + x2)). Find the linear equations of the tangent plane in R4 to the graph of F at the point (PI/4, PI/4, 0 , 0 ) The attempt...

Homework Statement On sheet Homework Equations On sheet The Attempt at a Solution On sheet

1. Two objects are connected via a pulley and some string. The 12 kg cart is on a frictionless 42 deg. incline while the 15kg block is on a horizontal surface having a coefficient of friction equal to 0.23. Determine the acceleration of the system of masses. 2. Fnet=ma 3. I first...

Homework Statement I am pursuing conceptual help regarding electric field due to uniformly charged planes. Homework Equations E=\frac{\sigma}{2\epsilon} The Attempt at a Solution I understand that a capictor has plates that are +/-Q. However, how would you calculate the elctric...

If I have cubic structure where plane is define by vector \rho and in z direction I have planes ...m-2,m-1,m,m+1,m+2... and if I have for example \sum_{m,\vec{\rho}}\hat{B}_{m,\vec{\rho}}\hat{B}_{m+1,\vec{\rho}} how to go with that in K-space? If I...

Homework Statement Consider three planes P1, P2 and P3 where a, b and c are constants. Plane 1 : x + 2y − z = 5 Plane 2 : ax + y + z = −2 Plane 3 : bx − 2y + cz = 11 1) Find the constants a, b and c such that the three planes intersect in a single point 2) For which values of d and...

I have to find two planes z=f_1(x,y)=a1*x+b1*y+c1 z=f_2(x,y)=a2*x+b2*y+c2 That satisfy: 1. both planes go through (-5,9,8) 2. the intersection line between the planes is located outside of the Cylinder x^2+y^2=4 3. the surface area of x^2+y^2=4 that is bounded between f1 and f2 is...

1. An 80.0 kg box is pushed up a frictionless incline. Hypotenuse = 10.0 m. Opposite = 7.0 m. How much work is done on the box moving it to the top?