Intersection Definition and 688 Threads

quick shpere intersection question?? Homework Statement Use the given info to answer the following questions a. find an equation of the sphere with the give center and radius. center (1,-11,3) radius 5 answer is (x-1)^2 + (y+11)^2 + (z-3)^2 = 25 where I am stuck is the next...

How do i get the point of intersection of a line and a circle.. I got lots of information on this topic, but my requirement is not matching.. I got a line whose one end point lies at the origin of the circle.. and other end lies somewhere outside the circle.. Now i need the point of...

Homework Statement Find the volume of the intersection of two spheres of radius 2, give that the center of each sphere lies on the surface of the other. The Attempt at a Solution I was trying to do this problem with volumes of revolution. I drew two circles, one with a center at -1, the...

Hi, I'm reading HL Royden's real analysis, though my question pertains more to set theory. Let X be a set. Then the intersection of an empty collection of subsets of X is equal to X. I understand this is not an intersection of empty subsets but it is still very counter-intuitive. Can...

Homework Statement Parametrize the intersection of the paraboloid z = x2 + y2 and the plane 3x -7y + z = 4 between 0 \leq t \geq 2*pi When t = 0, x will be greatest on the curve.Homework Equations The Attempt at a Solution I never really know how to do these kinds of problem. I am more...

Homework Statement Prove that the intersection of any collection of subspaces of V is a subspace of V. Okay, so I had to look up on wiki what an intersection is. To my understanding, it is basically the 'place' where sets or spaces 'overlap.' I am not sure how to construct the problem...

hi, I need to find the points of intersection between two cubes, and the algorithm should give the intersection points even though my cubes are rotated in any direction. i need to know, Is there any general algorithm for this and what is the current research(any method) in finding the...

Why is this true: (A - B) union (B- A) = (A union B) - (A intersection B) wouldn't the union of A and B everything that is in A or B? And since A - B and B - A don't contain any elements from the other set, wouldn't the union of these be equal to union of A and B? So wouldn't it make sense...

Homework Statement The vertex of the parabola y^2=2px is the center of an ellipse. The focus of the parabola is an end of one of the principle axes of the ellipse, and the parabola and ellipse intersect at right angles. Find the equation of the ellipse. Homework Equations...

Homework Statement 2x-y-z=3 and x+2y+3z=7 Homework Equations The Attempt at a Solution Im stumped on this problem because initially i thought all i had to do was make z, or another variable zero and then just solve. However, it then turns into a nasty problem. Most of the...

urgent, intersection of two planes Homework Statement Find the equation of the intersection between 2x + 3y - 4z = 12 and 5x + 2y + 3z = 7. Homework Equations none. I don't know how to use cross products, but is there another way? The Attempt at a Solution I don't know...

Volume of the intersection of two cylinders by cylinderical co-ordinates Homework Statement find Volume of the intersection of two cylinders by cylindrical co-ordinates The Attempt at a Solution IN the attached file I found it's 8(a^3)/3 It should be 16 not 8

Homework Statement **NOTE: One coordinate unit = 1000 feet. Also, the helicopter and the airplane are TWO SEPARATE moving vehicles.** At noon (12:00 PM), a helicopter is observed from point A (7, 0, 0) in the direction of vector -4i + 2j + 5k, and simultaneously from point B (0, 4, 0.25) in...

Homework Statement Given a set A \in R^m, B_n \in R^m for n \in N, show that A \ Union {from n = 1 to inf} B_n = Intersection {from n = 1 to inf} (A \ B_n} Homework Equations Same equation as above The Attempt at a Solution I think I have a solution in mind, but I wanted to...

I have a program to define union and intersection on 2 sets. I know I need 2 different input files, but other than that, I'm clueless.

Homework Statement Parameterize the curve of intersection of the cylinder x^2 + y^2 = 16 and the plane x + z = 5 Homework Equations The Attempt at a Solution i think i must first parameterize the plane x = 5t, y = 0, z = -5t then i think i plug those into the eq. of the...

Hey everyone! I recently picked up a motorcycle for class/work commutes because walking home at 11pm from the lab is not fun. But I have come across something of interest. Some intersections keep a green light on the main street and red on cross streets until a car pulls up. Before...

Homework Statement I am trying to solve this problem: Let W_1, W_2, W_3 be subspaces of a vector space, V. Prove that W_1 ∩ (W_2 + ( W_1 ∩ W_3)) = (W_1 ∩ W_2) + (W_1 ∩ W_3). Can someone help me show this? I have tried using Dedekind's law, but not sure it that is the way to go. The...

Hello. I am creating an algorithm for finding the locations of nodes connected by rigid links. Some nodes in the system are constrained in place, and to one node (a *special* node), a displacement is applied. The algorithm should be able to determine the locations of the other nodes by...

Homework Statement find the point closest to the origin on the curve of intersection of the plane 2y+4z=5 and the cone z^2=4x^2+4y^2 Homework Equations The Attempt at a Solution see 40 attachement. I found the used f(x,y,z)=x^2+y^2+z^2 and found its gradient. found ggrad and...

Homework Statement Solve the system of the linear equations and interpret your solution geometrically: 2x + y + 2z - 4 = 0 [1] x - y - z - 2 = 0 [2] x + 2y -6z - 12 = 0 [3] The Attempt at a Solution I've tried to eliminate the y variable: [1] + [2] 3x + z - 6 = 0 [4]...

The problem is finding the points of intersection for two given functions. f1=sin(-\pi*x) f2=1+cos(-\pi*x) I've plotted the functions using Maple. http://dl.getdropbox.com/u/12485/plot.png And I'm quite certain that to find the points of intersection, I have to set f1=f2 which...

Homework Statement 1) x=3+t y=2-4t z=-5+11t 2)12x+10y-4z Find the point where these two lines intersect. please help!

V1={cx^3+ax^2|c,a exists in R} V2={dx^3-bx^2 -d|d,b exists in R} find all the values of a,b that f(x)\epsilon V1\cap V2 ?? find all the values of a,b that f(x)\epsilon V1+ V2 ?? i know how to solve such question using vectors but they are not using using vector but some hoe check the...

There's a theorem that says any nested sequence of compact sets in Rn always has a non-empty intersection. So there is something wrong with this counterexample. I'm not able to see what's wrong: Consider the interval Un = [2-1/n, 1+1/n] for n=1, 2 and 3. Isn't the intersection of U1, U2 and...

we can prove that: the intersection of a finite number of open sets is open. how about: the intersection of any number of open sets? it's maybe not open.but how to prove it or the example? :smile:

Find the points of intersection of the lines... L1: R = 2i + 3j + 3k + t(i - 2j + 5k) L2: (x + 3) / 2 = (y + 1) / 2 = -z (I assume the plural in points is wrong... since that would be impossible) R, i, j, k are vectors; x, y, z are not --- x = 2 + t y = 3 - 2t z = 3 + 5t for some value(s) of...

: I hope this is not too dumb. I am kind of unclear on some issues: i) I understand that every bilinear map over a fin. dim. V space /F has a matrix representation (depending on the choice of basis ). Still, the intersection form ( in an orientable 4-mfld M.) is a map...

find the general equation of a plane that passed through the line of intersection (PQ) of 2x-7y+5z+1=0 and x+47-3z=0 find the equation of the particular plane through PQ which is parralel to the line x/-1 = (y-1)/3 = (z-3)/13 ok i think there is a couple of ways of doing this,this is the...

The Two Planes 2x-7y+5z+1=0 and x+4y-3z=0 intersect in a line PQ. What is the general equation of a plane through this line? Have done cross product of the two normals to get vector form of the line, and parametric x,y and z. Would like advice on what to do next, Thanks

Give an example where (A1 intersect A2)X(B1 intersect B2) is strictly contained in (A1XB1)intersect (A2XB2). For the union instead of the intersection I can see the reverse strict containment easily just by drawing. But for the intersection for some reason, I cannot see when the containment...

Homework Statement Say I have a sphere with the equation: (x-4)^2 + (y-3)^2 + (z+2)^2 = 20 How do I find the intersection with the xy-plane? Is the intersection at a point or it forms a circle Homework Equations The Attempt at a Solution Hmm.. I tried to set z equal to 0 to solve this...

Homework Statement Determine the points of intersection for the following equations f(x) = 2x/pi f(x) = sin x Homework Equations None The Attempt at a Solution In order to find the points of intersection you set the two equal to each other then find where x is equal to 0. I'm...

Homework Statement Find the vector equation of the line through 4,5,5 that meets (x-11)/3=7+8=z+4 at right angles Homework Equations The Attempt at a Solution i have no idea where to start.

Homework Statement Find value of k so that x+2y-z=0 x+9y-5z=0 kx-y+z=0 intersect in a line Homework Equations The Attempt at a Solution multiply l1 by 5 subtract l2 from 5l1 end up with: 4x+y=0 subtract l1 from l2 end up with: 7y-4z=0 i have no idea what to do from...

Homework Statement Simplify the expression: (B union C) intersection (B union NOT-C) intersection (NOT-B union C) The Attempt at a Solution I have no clue how to attempt this question, as every time I do attempt it I get a different solution.

Homework Statement I have an ellipsoid with center (000). There is a point A inside the ellipsoid with known coordinates(1,2,3) I draw a line from center to point A and extend it to cut the ellipsoid on on point p(x,y,z). Homework Equations I want to find the...

If V1 and V2 are both subspaces of a vector space V, then in order for their tensor product to be defined, does the intersection of V1 and V2 have to be 0?

Hello, how to prove this: V^{\bot}\cap W^{\bot}=(V+W)^{\bot} Thanks

This is not homework, just a toy problem I was thinking about. Let's say you have two spheres, one larger than the other. The center of the smaller sphere is placed on the surface of the larger sphere. How would you find the volume of the intersection?

Homework Statement Find symmetric equations for the line of intersection of the planes Homework Equations 5x - 2y - 2z = 1 4x + y + z = 6 The Attempt at a Solution I interpret this problem to say that I need to find a line of intersection of the two planes. I think I add them together and...

Homework Statement let A_{1}, A_{2}, ... be a sequence of subsets of R such that the intersection of the A_{1}, A_{2}, A_{3}..., A_{n} is nonempty for each n greater than/equal to 1. Does it follow that the intersection of all A_{n}'s is nonempty? Does the answer change if you are given...

Homework Statement Prove that the intersection of any set of ideals of a ring is an ideal. Homework Equations A nonempty subset A of a ring R is an ideal of R if: 1. a - b ε A whenever a, b ε A 2. ra and ar are in A whenever a ε A and r ε R The Attempt at a Solution My guess is...

Homework Statement The planes 5x-2y-2z = -1 and x-4y+2z = 25 are not parallel, so they must intersect along a line that is common to both of them. The vector parametric equation for this line is ... The Attempt at a Solution Ugh... this is a doozie... So I started the problem by...

I am looking to test detect if a cone (described by an apex, angle theta and axis) and a sphere (defined by a sphere centre and a radius) intersect. Please see here for a complete description (because i can't post the code here)...

Let H and K be subspaces of a vector space V. Prove that the intersection K and H is a subspace of V. Intuitively I can see that this is true... Both H and K must be closed under vector addition and scalar multiplication so there intersection must also be closed under both those. How do i...

Homework Statement At what point do the curves r1(t) = <t, 1 - t, 3 + t^2> and r2(s) = <3 - s, s - 2, s^2> intersect? Find their angle of intersection correct to the nearest degree. Homework Equations The Attempt at a Solution I set t = 3 -s 1 - t = s - 2 3 + t^2 = s^2 I got...

I'm stuck ... Ive proved the intersection of any number of closed sets is closed ... and Let S = { A_a : a Element of I } be an collection of compact sets...then by heine Borel Theorem ...Each A_a in S is closed...so this part is done now I just have to show the intersection is bounded...

(Problem from practice math subject GRE exam:) At how many points in the xy-plane do the graphs of y=x^{12} and y=2^x intersect? The answer I got was 2, but the answer key says 3. Intuitively, by the shape of their graphs, I would say two. I tried to calculate actual values for x...

I'm trying to do a simple electric field due to point charges problem, but I'm stuck on a very simple detail. There are a number of point charges on an xy plane, and one of the point charges is at the cooridinate (1,-2). I need to figure out which angle a line drawn from this point to the...