Intersection Definition and 688 Threads

Homework Statement Draw the axial force, shear force and bending moment diagrams. Show the locations and magnitude of the maximum and minimum values. Homework Equations See diagram. The Attempt at a Solution I've worked out the values from points A-B and then from points B-D. I...

Intersection of line and plane! Homework Statement Intersection of line and plane! Okay i to find the common points of line and plane Question r=i+j+A(2k-j) and r . (i+j) = 4 Homework Equations I heard that it is easier to use the vector equation in the form r . n = p The...

HELP! Intersection of two lines (VECTORS) Homework Statement Find the common point of the lines r=i+j+k+x(j-3k) and r=i+y(k-j) Homework Equations The Attempt at a Solution If the lines intersect then there are numbers x and y such that i+j+k+x(j-3k)=i+y(k-j) The two...

Hi, I have two 2D functions (surfaces), s1(x,y) and s2(x,y) defined via Interpolation. They intersect forming an intersection seam (which is a line). I can plot both functions using Plot3D and I can also plot the seam on the same 3D plot by means of the MeshFunctions option. The comand I...

Hi, All: The intersection form ( , ): H_n(M,R)xH_n(M,R)-->Z ; Z the integers and R any coefficient ring, in a 2n-manifold is well-defined in homology, i.e., if (x,y)= c , and x~x' and y~y' , then (x',y')=c Still, how is the value of the intersection form affected by changes in...

I need to find the point of intersection of the curves x^2 + y^2 =1, z= 0 and x=cost, y=sint, z=t. I plugged in the latter equation into the former and got (1,0,0) as an answer but I'm not exactly sure why that works, I can't visualize how plugging in the parts of a parametric equation will...

Homework Statement I need to find the 2 points of intersection (in polar form) of the two curves. I know just by looking that the origin will be one of the points, (0,0) The Attempt at a Solution I have approached this two different ways, 1. set them equal to each other and tried to...

What does a surface in R3 that intersects plane x = y at a line for every value of x represent? My first intuition is that it represents a plane because in R3 planes intersect at lines but I feel like there is a counterexample to this.

Hi, All: Given manifolds M,N (both embedded in $R^n$, intersecting each other transversally, so that their intersection has dimension >=1 ( i.e. n -(Dim(M)-Dim(N)>1) is the intersection a manifold? Thanks.

Hi, I keep seeing this come up A1 ⊇ A2 ⊇ A3 ... is an infinite decreasing sequence of events. Prove from first principles that P(intersection of Ai from i=1 to infinity) = Lim P(An) as n--> infinity All i can think of is that since each is a subset of the preceding, then A1 ∩...

Homework Statement Find the parametric equations of the intersection line of two planes 2x - 3y - z + 1 = 0 and 3x - 2y + 3z - 4 = 0 Homework Equations N/A The Attempt at a Solution First I'll label them: 2x - 3y - z + 1 = 0 [1] 3x - 2y + 3z - 4 = 0 [2] Then I get rid of the...

Homework Statement If i have 3 balls of radii =2 and centres =(1,0,0),(0,1,0) and (0,0,1). Find the volume of the intersection of the three balls. Homework Equations The Attempt at a Solution The only method i know only works when the first ball has a centre at (0,0,0) and the...

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

Hi Taking the intersection of a n-cube with any hyperplane, i would like to know the maximum number X of non adjacent vertices of the cube lying in such intersection. In R2 for instance, i can cut the unit square {(0,0),(1,0),(1,1),(0,1)} with a diagonal line passing through (1,0) and...

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 -...

Homework Statement I'm trying to find when that parametric curve intersects with the line x=20 Homework Equations x(t)=(2t^3)/(t^2-1) ; y(t)=(2t^3)/((t^2+1)^2) The Attempt at a Solution I tried representing the line as y=t ; x=20 35=2t^3/(t^2-1) ; t=2t^3/((t^2+1)^2) I also ended up with...

Hi, Everyone: Sorry if this is too simple: I guess the intersection for for CP^2 (complex projective 2-space) is (-1), right?. Since H_2(CP^2,Z)=Z, which is represented by CP^1, which has self-intersection=-1. Then, if we had a connected sum of CP^2's, the intersection form...

1. A better way to find the point of intersection of two lines is parametrically as two linear interpolations b/w inital and final points. x=(1-s)x1+sx2 y=(1-s)y1+sy2 where x1 and y1 are the inital points and x2,y2 are the final points. (-6,-6) (5,2) x=(1-t)x3+tx4 y=(1-t)y3+ty4...

Homework Statement Prove that the curve \vec{r}(t) = <cost,sint/sqrt(2), sint/sqrt(2)> is at the intersection of a sphere and two elliptic cylinders. Reparametrize the curve with respect to arc length measured from (0, 1/sqrt(2), 1/sqrt(2)) in the direction of increasing t. Homework Equations...

1. At what points does the curve r(t)=ti+2tj+t2k intersect the surface z = x2+y2-100? Give the coordinates of the points. 2. Given equations above. 3. r(t)=<t, 2t, t2> z = x2+y2-100 (t2) = (t)2+(2t)-100 -4t2 = -100 t = sqrt(25) = +/- 5 when t = 5, (5, 10, 25) when t = -5 (-5, -10, 25) This...

Homework Statement Show -0.25 <= P( X \cap Y ) - P( X )P( Y ) <= 0.25 for any events X, Y Homework Equations P( X \cap Y ) = P( X )P( Y | X ) Bayes' theorem Anything I missed? The Attempt at a Solution Obviously if X and Y are independent P( X \cap Y ) = P( X )P( Y )...

Hi, Everyone: Just wondering if anyone knew about how to work with the intersection form with coefficients in Z/2. I only know this is in relation to Wu's vector, tho I don't know what Wu's vector is. I was also hoping to know if the intersection form for (4n+2)-manifolds...

Hi, Everyone: I am trying to understand the meaning of a statement that two embedded manifolds intersect normally*. The statement is made in a context in which any choice or existence of a metric is not made explicit, nor--from what I can tell-- implicitly either. If...

Two tangents to an ellipse meet at a point T, find the coordinates of T. The two equations are (bcosΘ)x + (asinΘ)y= ab (-bsinΘ)x + (acosΘ)y= ab This has been really frustrating me as I feel it should be simple, but with the trigonometric...

Homework Statement At how many points in the xy-plane do the graphs of y=x^{12} and y=2^{x} intersect? Homework Equations none The Attempt at a Solution I have no idea what to do. I thought of trying to narrow it down to some intervals where the graphs may cross, but, since they're...

Homework Statement I'm given two subspaces L and K of P2 (R) are given by L = { f(x) : 19f(0)+f ' (0) = 0 } K = { f(x) : f(1) = 0 }. Obtain a non-trivial quadratic n = ax2 + b x +c such that n is element of the intersetion of L and K. Homework Equations The...

Homework Statement If V and W are 2-dimensional subspaces of \mathbb{R}^{4}, what are the possible dimensions of the subspace V \cap W? (A). 1 only (B) 2 only (C) 0 and 1 only (D) 0, 1, 2 only (E) 0,1,2,3, and 4 Homework Equations dim(V + W) = dim V + dim W - dim(V \cap W) dim (V + W) \leq...

Hello all, Given two 3D lines described by the general equation \vec{L(t)}=\vec{p}+\vec{d}t I found a way to find their intersection point, but it uses the cross product in the derivation. I am assuming a 4D line is a valid thing? And can be described the same way? (except with 4 element...

I have two metal bars positioned in space so that, when viewed in the xy-plane, they intersect each other at some point P. One of the rods are parallel with the x-axis and at rest, while i move the other rod downwards, in the -y direction, with a speed u. The speed of the point P, called U_P...

Homework Statement Show that the intersection of Ai (for all i in I = {1, 2, 3, ... n } = A1. Ai is a subset of Aj whenever i <= j.Homework Equations The Attempt at a Solution Show: ***I'm having trouble showing part 1***1. that the intersection of Ai is a subset of A1, and 2. A1 is a subset of...

Prove that the intersection of any collection of closed sets in a topological space X is closed. Homework Statement Homework Equations The Attempt at a Solution

I am looking to find a vector which does not lie in various subspaces. For example, if I have: S1 = [1,0,0; 0,1,0] (x-y plane) S2 = [1,0,0; 0,0,1] (x-z plane) S3 = [0,1,0; 0,0,1] (y-z plane) I want to find a vector which was not within any of these subspaces - in this specific example...

Homework Statement Prove that the intersection of a number of finite convex sets is also a convex set Homework Equations I have a set is convex if there exists x, y in the convex S then f(ax + (1-a)y< af(x) + (1-a)y where 0<a<1The Attempt at a Solution i can prove that f(ax + (1-a)y) <...

Dear Friends, I have below query Available data: Point1 (r1,theta1,phi1) Point2 (r2,theta2,phi2) where in spherical coordinate system r(i)=radius theta(i)=angle phi(i)=azimuth Required output: Line of intersection by individual planes generated by each point i.e. from point1 we...

Homework Statement Consider the plane z = x + 2y and the cylinder x^2 + y^2 = 1 (a) Find a vector function r(t) describing their intersection. (b) Find the points if any where the tangent to ~r is horizontal (c) Find an equation for the tangent line to ~r at each of these points.Homework...

Homework Statement let V be a finite dimensional vector space of dimension n. For W \leq V define the codimension of W in V to be codim(W) = dim(V) - dim(W). Let W_i, 1 \leq i \leq r be subspaces of V and S = \cap_{i=1}^{r}W_i. Prove: codim(S) \leq \sum_{i=1}^{r} codim(W_i)Homework...

Homework Statement Let A, B be sets, C,D\subset A and f:A\longrightarrow B be a function between them. Then f(C\cap D)=f(C)\cap f(D) if and only if f is injective. Homework Equations Another proposition, that I have proven that for any function f(C\cap D)\subset f(C)\cap f(D), and the...

Hi everyone, I'm reading Rudin's Analysis and in the topology section, he implies that the finite intersection of closed sets is not necessarily closed. (pg. 34) Can someone give an example of this? I can't seem to find one.

I need to graph/find numbers for S∩T where S is x^2+y^2 <=100 and T is x+y<=14. I know I can find them simply by choosing/picking them, but are there any other solution ? I thought maybe doing x^2+y^2 <=100 + x+y<=14 = x^2+y^2 + x+y<=14 +100 = x^2+y^2 + x+y<=114 = x^2+y^2 <=...

f: A-->B is a function. A,B are sets. Let A1, A2 be contained in/equal to A. f(A1 intersection A2) is contained in OR equal to f(A1) intersection with f(A2). Show that the equality holds if f is an injection. I know how to prove that it is contained, but not the equal/injection part...

Homework Statement Show that for 3 events A, B, C, the probability P of the intersection of A, B, and C is greater than or equal to P(A) + P(B) + P(C) - 2. aka: P(A intersection B intersection C) > or = P(A) + P(B) + P(C) - 2 Homework Equations N/R The Attempt at a Solution Use...

Homework Statement When a plane intersects a sphere at more than two points, it is a circle (given). Let x^2+y^2+z^2=1 be a sphere S, and P be a plane that intersects S to make a circle (called C). Let q:[a,b] -> R^3 be a unit speed parameterization whose trace is C. Prove that the second...

Hello, How can I determinate the intersection points of these equations: 1-(2/a)x and +- Exp(-x) It's from an exercise on quantum mechanics where I don't know why the gradient of the exponential is -1. YThanks

Homework Statement The plane x+y+z=1 cuts the cylinder x^{2}+y^{2}=1 in an ellipse. Find the points on this ellipse that lie closests to and farthest from the origin.Homework Equations N/AThe Attempt at a Solution first step was to determine the intersection of the plane and the cylinder. so...

Homework Statement Hi, i am trying to do the question on the image, Can some one help me out with the steps. [PLAIN]http://img121.imageshack.us/img121/6818/algebra0.jpg Solution in the image is right but my answer is so off from the current one. Homework Equations The...

I'm trying to understand the proof given in the last 10 minutes or so of this video lecture, but after some struggle, it occurs to me that I may be misinterpreting what the theorem says. According to this, Cantor's finite intersection principle states the following. Given a metric space (X,d)...

Let H and K be normal subgroups of G such that H intersect K=<e>. Show that hk=kh for all h in H and k in K. H and K are normal so ghg^-1 is in H and gkg^-1 is in K. want to show hk=kh. So basically I'm showing this is abelian. Can I do ghg^-1=gkg^-1? ghg^-1g=gkg^-1g gh=gk so that works if g=h

Heres the question: Let {u,v,w} be a linearly independent set of vectors of R^4. Let E = span{u,2v} and F=span{w,v}. Find EnF and E + F. i really have no idea other than i guess if 1/2u=w and v=v, then the EnF can be defined by that, but I'm not sure if that is right! :(

Hi, everyone: This should be easy, but I am having trouble with it. I am rusty and trying to get back in the game: Let Q(a,b) be an intersection form in the middle homology class of some 2n-manifold. What is the geometric difference between Q(a,b) and Q(b,a).? If n is even...