Intersection Definition and 712 Threads

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...

show that U intersection W does not equal ((0,0,0)) and hence that U+W is not a direct sum U being (a,0,a) and W being (c,d,c+2d) and we know that c d and a are elements of R, why are there not a direct sum? is there a rule that prevents any of a c or d from being the zero vector? if this is...

Determine wether the lines L1, L2 are parallel, skew or intersecting. If they intersect, find the point of intersection. L1 = \left(\begin{array}{ccc}x\\y\\z\end{array}\right) = \left(\begin{array}{ccc}1\\2\\0\end{array}\right) + t \left(\begin{array}{ccc}1\\-1\\3\end{array}\right) L2 =...

Homework Statement Solve for the vector function that represents the curve of intersection in the following two surface: z = sqrt(x^2 + y^2) and z = 1 + y Homework Equations The Attempt at a Solution Through blind trial and error, I managed to get the book-specified answer of x =...

Homework Statement If H, K are subgroups of G, show that H intersect K is a subgroup of H Homework Equations I know that H intersect K is a subgroup of G; I proved this already but I'm wondering how H intersect K is a subgroup of H The Attempt at a Solution I'm quite sure this is true...

Homework Statement Hello, as part of a computer science project, I have been tasked with writing an application that will generate an involute spur gear based on given criteria. To do this, I will need to be able to find the point of intersection between the involute curve (used to define...

Here is the problem: Replace the two forces afting on the pole by a wrench. Write a moment M associated with a wrench as a vector and specify the coordinates of the point P in the y-z plane through which the line of action of wrench passes. I already figured the moment to be ("T" and "a"...

Homework Statement You are driving a car at the 25-mi/h speed limit when you observe the light at the intersection 70 m in front of you turn yellow. You know that at that particular intersection the light remains yellow for exactly 4.0 s before turning red. After you think for 1.0 s, you then...

Homework Statement Given A1 superset of A2 superset of A3 superset of A4 ... and so on how can i construct sets B1, B2, ... so that each Bi's are disjoint. The goal is to get the infinite intersection of Ai = the infinite union of BiHomework Equations De morgans law: (AUB)^c = (A^c N B^c)...

Homework Statement Prove that: A is a subset of B if and only if (A intersection B)=A Homework Equations The Attempt at a SolutionI tried proving the right side, that is (A \cap B)=A For two sets to be equal then they have to be subsets of each other...so: (A \cap B)...

1. Homework Statement http://www.nellilevental.com/calc1.jpg 2. Homework Equations C1 = \left(x - 1\right) ^{2} + y^{2} = 1 C2 = x^{2} + y^{2} = r^{2} 3. The Attempt at a Solution Initially I thought that the "value" of R was just going to increase without bound since the...

Consider the two lines L1: x=-2t y=1+2t z=3t and L2: x=-9+5s y=36+2s z=1+5s Find the point of intersection of the two lines. My teacher said that I should use system of equations to solve for the point, but I am sort of confused on what to do because there are 2...

I'm working out of Abbott's Understanding Analysis and I'm trying to show the following, For an arbitrary function g :\mathbb{R}\longrightarrow \mathbb{R} it is always true that g(A\bigcap B) \subseteq g(A) \bigcap g(B) for all sets A, B \subseteq \mathbb{R}. I'm confused on how to get...

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). I have answered the question but I am not sure it is correct; if someone can review it their comments would be appreciated...

Homework Statement The graphs of f( ) = 2sin() - 1 (blue) , and g() = 3cos() + 2 (red) are shown below: http://img403.imageshack.us/img403/6991/38ah7.jpg http://g.imageshack.us/g.php?h=403&i=38ah7.jpg What equation would have the intersection points of the graph its solutions...

Say there's a family of set M with infinitely many elements with the property that whenever X and Y belong to M, so does their intersection. How to justify that the intersection of all elements in in M, N, (interpreted here as the largest subset common to every element in M) is also in M? Since...

I'm trying to work through an explanation of how a ray-sphere intersection can be solved algebraically from here: http://wiki.cgsociety.org/index.php/Ray_Sphere_Intersection My problem is at this step: I don't understand how they've expanded the formula. I thought you just multiplied...

Homework Statement hey guys ok basically i have 2 questions, first one is (1) "find the point on the curve y=(x-1)[power of 5] +2 where the tangent to the curve at these points is parallel to the x axis" Attempt : well the gradiet of the x-axis is 0. So i differentiated the...

I am very confused about the problem presented below and would appreciate any help in visualization or pointing me in the direction of an article or equation that will set me on the right path. I can't seem to get past the initial set up of the problem at this point and am quite frustrated at...

Homework Statement You are diving to the grocery store at 20 m/s. You are 110 m from an intersection when the traffic light turns red. Assume that your reaction time is 0.70 s and that your car brakes with constant acceleration. A) How far are you from the intersection when you begin to...

Homework Statement Find the vector, parametric and symmetric equations of a line that intersect both line 1 and line 2 at 90°. L1 : x = 4 + 2t y = 8 + 3t z = -1 - 4t L2 : x = 7 - 6t y = 2+ t z = -1 + 2t Homework Equations \vec{a}1 - \vec{a}2 + \vec{b}1t - \vec{b}2s...

Homework Statement Solve the following systems and interpret the result geometrically 3x + 4y + 5z - 18 = 0 2x - y + 8z - 13 = 0 -x + 17y + 25z + 11 = 0 Homework Equations The Attempt at a Solution I've been working on this problem for a while, The first thing i did was find...

Homework Statement Find the point of intersection of the line and the plane. Line: x=4+k y=2-2k z=6+3k Plane: x=-1-s+2t y=1-s+4t z=2+3s+t Homework Equations None. The Attempt at a Solution So I'm not that well informed with how...

Homework Statement Find the equation of the plane which passes through the line \frac{x-2}{3}=\frac{y-3}{1}=\frac{z+1}{2} and it is normal to the plane x+4yy-3z+7=0 Homework Equations The Attempt at a Solution I find the intersection point of the plane and the line. It is...

Homework Statement Find the projection of the intersection between the two surfaces S1: z = 4-x^2 - y^2 and S2: 4x^2y = 1 (x>0) in the xy-plane 2. The attempt at a solution 4-x^2 - y^2 = 4x^2y -1 Is this all I need to do?

Hello. Right now: we're learning about derivatives. And the questions reads: Determine the coordinates of two points of tangency to the curve y=-2x^2, given that the corresponding tangent lines intersect at (2,8). What I know: I know that the derivative of the function is y'= -4x I know...

Homework Statement The curves `bar r_1(t) = < 2t,t^(4),5t^(6) >` and `bar r_2(t) = < sin(-2t),sin(4t),t - pi >` intersect at the origin. Find the angle of intersection, in radians on the domain `0<=t<=pi`, to two decimal places. The Attempt at a Solution Well, I tried to do it in...

I've been having a problem finding the intersection points of the following polar equations. r=1+3sin(theta) and r=1-3cos(theta) Now I've set the equations equal to each other to obtain those points. I've set each equation equal to zero. The problem I'm having is that when graphed...

Homework Statement Prove that the lines r=(a,b,c)+t(d,e,f) and q=(h,i,j)+s(k,l,m) intersect, and find the coordinates of their point of intersection. Also, find the acute angle between their lines Homework Equations The Attempt at a Solution I have no attempt because I'm stumpped...