Intersection Definition and 712 Threads

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...

How to show that a transverse intersection is clean, but not conversely?

Homework Statement The surfaces S1 : z = x2 + y2 and S2 : x2 + y2 = 2x + 2y intersect at a curve gamma . Find a tangent vector to at the point (0, 2, 4). Homework Equations i thought about finding gradients of the two functions and plug in the given point in the gradients and cross...

Hi, Everyone: The intersection form q(a,b) in dimension 1 (i.e., in H_1(K) , for any top. space K) is symplectic/alternating , meaning that q(a,b)=-q(b,a). From this last, it follows that q(a,a)=0. How do we interpret this last.?. Does this imply that any curve in any...

Two cars approach each other at an intersection. One car has a mass of 928.4 kg and is traveling in the negative y direction with a velocity of 21.4 m/s. The second car has a mass of 951.2 kg and is traveling in the positive x direction with a velocity of 39.5 m/s. If the collision is totally...

y=x^3-2x+1 y=x^2 The question says to use the bisection method to find the points of intersection of the 2 curves. I know how to use the bisection method to find the root of an equation (like on this page http://kr.cs.ait.ac.th/~radok/math/mat7/step7.htm ), but how would I use it to find...

I know the union can be, but how about the intersection? I am trying to prove that: Suppose (X,T) is a finite topological space, n is a positive integer and U_i\in T for 1<= i <= n. Use mathematical induction to prove \bigcap U_i \in T, where the intersection goes from i=1 to n.

Show the intersection of complex sphere (|z1|^2+|z2|^2+|z3|^2=1) in C^3 and the complex cone (z1^2+z2^2+z3^3=1) in C^3 is a smooth submanifold of C^3. I am trying to do it using regular level set, but I am not sure which one of (1,0) or (1,1,0) should be set to be the regular value?

Hello! I have a quick question regarding the intersection of three planes if the determinant is 0. If there are solutions, there will be an infinite number of solutions. One of the equations for the plane can be ignored as it is a linear combination of the other two, and can be ignored for...

Homework Statement See first figure attached Homework Equations The Attempt at a Solution I was able to sketch the two curves individually to get an idea of what I'm looking at, but I still can't really visualize how the two curves would intersect each other in the first octant...

* Need help with "Finding the point of Intersection" - Thanks Homework Statement Can someone please explain how I would solve this: As in find the pair of the given lines point of intersection. L: x - y = 4 M: x + 2y = 7 Now, Do i have to turn these into slope intercept ? I know...

thought I understood equations of planes in R3 and their intersections, but apparently not. I'm very confused by what seems to be a basic problem: find a vector equation for the line of intersection of x + y + z= 0 and x + z = 0. Is x + z= 0 still a plane even though it doesn't have the...

Homework Statement Ok, I think i got it, but can you all tell me if these are the right/proper steps I must do? Determine the point of intersection of the following pair of lines: 3x - 7y = 8 2x + 4y = -12 Now, first step is the use the 2nd equation and turn the 2nd equation into...

Homework Statement Well, I must express this trajectory: \vec{r}=(t^2,2t,t^2) as an intersection of two surfaces. I really don't know how to work this. It seems to be some kind of parabola, but I'd really like to see some step by step for solving this. Bye, and thanks off course.

Figured it out.

To find the intersection of two lines in R3, you set the lines equal, right? [a,b,c] + d[e,f,g] = [h,i,j] + k[l,m,n] Then split these into three equations, 1. a + d(e) = h + k(l) 2. b + d(f) = i + k(m) 3. c + d(g) = j + k(n) And solve for k and d, correct? If k and d are consistent...

Parameterizing vector function for intersection of cylinder and plane Homework Statement Problem asks us to find the vector function of the curve which is created when the plane y= 5/2 intersects the ellptic cyl. (x^2)/4 + (z^2)/6 = 5 Homework Equations The Attempt at a...

Hi, I am having difficutly figuring out why the cross product of the normal vectors of each plane gives the direction vector of the line of intersection. Anyone care to try to explain? Thanks!

Homework Statement Find a vector parameterization of the intersection of the surfaces x2+y4+2z3=6 and x=y2 in R3. The Attempt at a Solution I let x=t. Then y3=t I solved the first equation for z in terms of x z = cube root ((t2+(t(cube rt(t)) - 6)/-2) I know this is wrong...

Are there any kinds of functions which satisfy f(A1 ∩ A2) =f(A1) ∩ f(A2)? Prove your claim.?

Homework Statement I need to locate the coordinates if a point of intersection x0,y0,z0 of a plane with equation 2x+y-z=0 and a line that is perpendicular to that plane and passes through a point G(2,1,0). Homework Equations and I understand that this is a normal line and a plane so...

Homework Statement Suppose f is a function with sets A and B. 1. Show that: I_{f} \left(A \cap B\right) = I_{f} \left(A\right) \cap I_{f} \left(B\right) Inverse Image of F (A intersects B) = Inverse Image of F (A) intersects Inverse Image of B. 2. Show by giving a counter example that...

Hi, I have been at this single problem for two hours with nothing to show for it. Find symmetric equations for the line of intersection of the planes. z = 3x - y - 7 z = 4x + 2y - 6 They also give me one of the symmetric equations, z/10. I have over 3 pages of work for this. I...

I am close to positive I am going at this problem the correct way, but there seems to be some error somewhere. This problem is from online homework. Homework Statement A hot-air balloon has just lifted off and is rising at the constant rate of 2.2 m/s. Suddenly one of the passengers...

Compute the intersection of a line and an ellipse centered at (0,0). Ellipse equation is b²x² + a²y² = a²b² where b is the minor axis and a is the major axis. I am having trouble finding A, B, and C- somewhere down the line, I know the Quadratic Eq. is used to find x. I also know AX² + BX +...

** I accidentally posted this in the pre-calc math section first, but I think it's more applicable here...sorry** Homework Statement I need to find the intersection point of two vectors. For vector A, I have it's start point (0,0,0) and it's magnitude in components (-.41, .28, -.08)...

Homework Statement I need to find the intersection point of two vectors. For vector A, I have it's start point (0,0,0) and it's magnitude in components (-.41, .28, -.08). For vector B, I only know it's start point (-2.70, -.45, -.21) I also know that the angle between the two...

Homework Statement Solve the following equation: e^{2x}=3x^2 Homework Equations The Attempt at a Solution I can find an approximate solution with a graphing calculator easily, but I am interested how you would find the exact solution. I can take the natural log of both sides...

I understand that the finite intersection of open set is open, but is it true that the infinite intersection of open set is closed? or is it possible for it to be open as well? Thank you, M

Homework Statement Show that the set of rational numbers in the interval (0, 1) cannot be expressed as the intersection of a countable collection of open sets. Homework Equations The Attempt at a Solution This sounds like something requiring proof by contradiction. There must be...

Would it be possible for something to pass through 2 event horizons,falling into both black holes? also,if it can,what would happen if the objecct in question (lets say a proton) was at a point where the forces acting on it were equal in every direction? say being at the centre of these two...

Hello all, I have the following question regarding the interchange between union and intersection. \cup_{q < t} \cap_{s > q} A_{s} = \cap_{s<t} \cup_{q<s} A_{q} = \cup_{q < t} A_{q} Am I correct? Also, can anyone provide me some more resources regarding this kind of interchange in...

Homework Statement Find any points of intersection of the graphs by the method of substitution. xy+x-2y+3=0 x^2+4y^2-9=0 Homework Equations The Attempt at a Solution From the second equation I can solve for y: y=\frac{\sqrt{9-x^2}}{2} Plug it into the first equation and...