Intersection Definition and 688 Threads

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...

Does anyone know how to determine whether two ellipses intersect? I don't need the precise points but rather only the answer whether there are points. All my attempts led to 4th order polynomials, which are heavy to solve, but considering that I don't need the actual points I assume there must...

Homework Statement A solid has a circular base of radius r=4. Find in each case the volume of the solid if all intersection between the solid and a plane perpendicular to a set diameter is: a) A square b) A triangle rectangle isosceles which one of its sides is on the circular base. The...

I'm having a little trouble distinguishing the line between what the f.i.p implies and what it does not. **EDIT2** Hopefully this will make things more clear What I'm really interested in is a formal definition of the f.i.p regardless of the set in question or the field. Given the sequence...

Homework Statement P1 = 3x+4y=1 P2 = x +y -z=3 Find the intersection. Homework Equations x = x0 +at y = y0 + bt z = z0 + ct The Attempt at a Solution I used a quicker method. I first did P1 x P2 and got its cross product <-4,3,-1> Then I followed what our teacher had shown us in class -...

I'm working on tracing the beam path of a HeNe laser through two prisms, and I'm stuck on trying to find the incident plane in which to use Snell's law. Basically I have the equation of the angled surface of the prism, and I have the point where the beam intersects that plane. Now I need the...

I know that intersection tests can typically (for hit detection in games) be computed in log n time with reasonable accuracy, but there is a problem that I see with using hierarchical bounding volumes in ray tracing. For example, a ray may intersect a bounding volume however due to the shape...

I have been asked if the following is true or false the intersection of two connected sets is connected ? I would have thought that if their intersection was empty they wouldn't be connected. If they were disjoint or course it would be empty. any ideas?

Homework Statement find the area inside both of the curves r = 4 cos@ r = 2+2cos@ @ = theta Homework Equations ------- The Attempt at a Solution i will say 4cos@ = 2+2cos@ to find the intersection points 4cos@ = 2+2cos@ 2cos@ = 2 cos@ = 1 @ = 0 ! I need the other points!

Let G_{n} = (-1/n,1/n) for all n in N let G= \bigcap^{\inft}_{n=1}

Hello all, I am neither a physicist nor a mathematician, I am an archaeologist trying to develop a mathematical model for archaeological site detection. The problem is set up like this (and hopefully this will make some sense): The detector moves in parallel transects that can be of any...

Homework Statement Prove that r1 and r2 intersect at (1,1,3). Let r1 and r2 be defined as: r1(t)=t^2i+tj+3t^3k r2(t)=(t−1)i+(1/4)t^2j+(5−t)k Homework Equations Intersection is derived from r1=r2. The Attempt at a Solution I only formally get to this point and then start...

Homework Statement Find the equation of the plane that passes through the line of intersection of the planes 4x - 3y - z - 1 = 0 and 2x + 4y + z - 5 = 0 and passes through A(1, -3, 2). Homework Equations N/A The Attempt at a Solution I have no clue on how to start this question...

Can you please give me formulas which give intersection of two gaussian function f(x, mu, sigma) = 1/sqrt(2*pi*sigma^2) * exp(-(x-mu)^2 / (2*sigma^2)) for the case variances are different. (Note: I think it is time I learn how to use "tex" tags, do you know a good tutorial?)

Homework Statement Find the slope of the tangent line to the curve of intersection of the vertical plane x - y + 1 =0 and the surface z = x2+y2 at the point (1, 2, 5) Homework Equations Gradients, Cross products The Attempt at a Solution I'm pretty lost here. I think I have to...

Homework Statement Does the surface z = x^2 + y^2 - 4 * intersects the yz -plane? If so, find the equation of the curve and write down the points of intersection. The Attempt at a Solution yz-plane, so x=0 1) * becomes z = y^2 - 4 and this is the equation of the curve that intersects...

Homework Statement Let S be the solid region bounded by the paraboloid z = x^2 + y^2 - 4 for z \le 0 , 0 \le x \le \sqrt{4 - y^2} and 0 \le y \le 2 . Find the Cartesian equations of the curves if the surface S intersects the xy,xz , and yz planes. The Attempt at a Solution...

Hi, everyone: How do we show that 2 planar surfaces in R^4 intersect at points (possibly empty sets of points, but not in lines, etc.). I am curious to see how we justify the Poincare dual of the intersection form in cohomology being modular, i.e., integer-valued...

Homework Statement Use a dounble integral to find the area of the region inside r = 1+ cos (theta) and outside r = 2sin (theta). sketch region and indecate the points of intersection. I'm confused how to find the points of intersection of these two equations Homework Equations I've...