Intersection Definition and 688 Threads

Homework Statement Describe and sketch the geometric objects represented by the systems of equations Homework Equations x2 + y2 + z2 = 4 x + y + z = 1 The Attempt at a Solution I can sketch both objects: 1) sphere with center (0,0,0) and radius 2 2) "simple" plane with intersection...

<Moderator's note: Moved from a technical forum and thus no template.> I am at the beginners level of linear algebra and having problem of the intersection of matrices. Your kind help is much appreciated for the following question Let\quad M1=\begin{Bmatrix} x & -x \\ y & z \end{Bmatrix},\quad...

Homework Statement Let ##\mathscr{F}## be a finite family of open or closed intervals in the line ##\mathbb{R}^1##. Show by an elementary proof that if any ##2## of them intersect, then all of them intersect. Homework EquationsThe Attempt at a Solution Here is my attempt, where for now I'm...

Homework Statement tl;dr: looking for a way to find the intersection of three cones. I'm currently working with a team to build a Compton camera and I've taken up the deadly task of image reconstruction. Background Theory: https://en.wikipedia.org/wiki/Compton_scattering For a single Compton...

Homework Statement Find equation of line of intersection of planes r.(3i-j+k)=1 and r.((i+4j-2k)=2 Homework Equations a x b gives a perpendicular vector to a and b...(i) The Attempt at a Solution to write equation of a line r=a+tb we need a point a on the line and a parallel vector b. Taking...

Homework Statement Let ##G## be a finite p-group and ##Z(G)## its center. If ##N \not = \{e\}## is a normal subgroup of ##G##, prove that ##N\cap Z(G) \not = \{e\}##.Homework EquationsThe Attempt at a Solution Since ##N## is a normal subgroup we can let ##G## act on ##N## by conjugation. In a...

Justify the following by using table, graph and equation. use words to explain each representation f(X) = 2 x2 - 8x and g(x) = x2-3x+ 6 the points (-1,10) and (6,24)

Homework Statement A train 400 m long is moving on a straight track with a speed of 21.6m/s. The engineer applies the brakes at a crossing, and later the last car passes the crossing with a speed of 5.0m/s. Assuming constant acceleration, determine how long the train blocked the crossing...

Homework Statement "Consider a cylinder with a generator perpendicular to the horizontal plane; the only requirement for a point ##(x,y,z)## to lie on this cylinder is that ##(x,y## lies on a circle: ##x^2+y^2=C^2##. Show that the intersection of a plane with this cylinder can be described by...

Hello, I believe that this is the correct forum for this post but please let me know if otherwise. I have the following data in R4, id x y z a B -0.0700177 0.382249 -0.289338 0.00349957 A 1.13388 1.77602 -0.679365...

Homework Statement From Linear Algebra and Its Applications, 5th Edition, David Lay Chapter 4, Section 1, Question 32 Let H and K be subspaces of a vector space V. The intersection of H and K is the set of v in V that belong to both H and K. Show that H ∩ K is a subspace of V. (See figure.)...

Hey, I have a couple of questions I've been doing online which have left me a little puzzled. The first one, I'm not really sure how to go about. I think a lot of that comes down to having not had a lot of experience with parametric forms. I'll just post screenshots of where I'm up to on...

Homework Statement Given l→1=(6,−1,0)+t(3,1,−4) and l→2=(4,0,5)+s(−1,1,5), find the intersection of l→1 and l→2 . Homework EquationsThe Attempt at a Solution I'm fairly certain I did this correctly, but I just thought I'd double check to make sure I have a good understanding.

does anybody know how to solve this problem ?Consider two trigonometric functions y = cos 2x and y = 1 + sinx.(a) Write down the equation in x that you would solve to find the x coordinate of point(s) of intersection of those graphs on [0, 2∏]. (b) Solve your equation, and write down the...

The only thing I wish to take from this graph is the intersect of the two lines of best fit. How can I get the uncertainty in this point? While the points appear to have the same uncertainties, they actually each have their own distinct % uncertainty. Would the maximum uncertainty in the X...

Homework Statement Find the point of intersection of the following lines, if it exists. Homework Equations None. The Attempt at a Solution I think the first step is to form 2 equations, but I'm not too sure.

i have an equation like this: Given m(B-V)= 1.2 +- 0.2 How do you calculate the uncertainty in T? (btw, I solve T using graphs by finding the intersection point) My idea was first to calculate T when m(B-V) =0.2, and I then calculate T when m(B-V)= 1.2 + 0.2(its uncertainty). and then find the...

Mod note: Moved from a technical forum section, so missing the homework template. @fab13 -- please post homework problems in the appropriate section under Homework & Coursework. I have the following exercise to solve : I have to find all the points on the surface ##x^2+y^2+z^2=36## (so a sphere...

Homework Statement I am looking for the line of intersection of two cylinders (x^2+y^=1 and x^2+z^2=1) to find the curve for a line integral. However, I am getting z=y, which is a patently false answer. Mathematically, it seems to work out though. Homework Equations x^2+y^=1 x^2+z^2=1 The...

Hey! :o Let $V$ be a $\mathbb{R}$-subspace with basis $B=\{v_1 ,v_2, \ldots , v_n\}$ and $\overline{v}\in V$, $\overline{v}\neq 0$. I have shown that if we exchange $\overline{v}$ with an element $v_i\in B$ we get again a basis. How can we show, using this fact, that the intersection of all...

Hello, This is a bit more complex than my previous post, but I don't think it qualifies for university level difficulty. Please move this to the appropriate forum if my assessment is not correct. I have 4 vectors in three space where each vector has its tail at the same point (point B). id...

Homework Statement No problem statement Homework EquationsThe Attempt at a Solution Let ##A = \{(x,y) ~|~ x \ge 0 \mbox{ or } y=0 \}## be a subspace, which can be shown closed, of ##\Bbb{R}^2##. If my calculations are right, isn't ##A \cap [(0,\infty) \times \Bbb{R} ] = (\{0\} \times...

Hi everyone! I'm a student of electrical engineering. At my math class, we were given a problem to solve at home. Now, from what I've managed to gather, this is a trick question, but I would like to get someone else's opinion on the task. It's also worth mentioning that parametrization is a...

Homework Statement If event A equals event B, then the probability of their intersection is 1. True or False? Apparently the correct answer is False. The Attempt at a Solution If A=B then they should overlap entirely and their intersection should be 1? The only way I see this working is if...

Homework Statement Let ##S_1## and ##S_2## be subsets of the vector space ##V##. Prove that ##span (S_1 \cap S_2) \subseteq span(S_1) \cap span(S_2)##. Given an examples of ##S_1## and ##S_2## for which equality holds and for which the inequality is strict. Homework EquationsThe Attempt at a...

OK just seeing if this is setup OK before I pursue all the steps I thot adding areas would be easier:cool:

I have an expression for a "line- to sphere intersection" that works: a = 1 + Ax^2 + Ay^2 b = 2*(-zs + Ax*(Bx-xs) + Ay*(By-ys)) c = zs^2 + (Bx-xs)^2 + (By - ys)^2 - R^2 This is part of a code in Matlab, and works fine. It is derived from substituting (x=Ax*z+Bx, y=Ay*z+By) into...

In physics are we going more mathematical?

Homework Statement For which m and n the lines are concurrent? ##r: \begin{cases} x & - & y & = & 1 \\ nx & - & y & - & 2z & + & m & + & 1 & = & 0\end{cases}## ##s: \begin{cases} x & - & nz & + & m & + & n & = & 0 \\ x & + & y & - & 2nz & + & 11 & = & 0 \end{cases}## Solving r gives me...

Homework Statement "Let ##U={p+r\sqrt{2}:p,r∈ℚ}## and let ##V={a+b\sqrt{7}:a,b∈ℚ}##. Show that ##ℚ⊆U∩V##. Then show that ##U∩V⊆ℚ## and conclude that ##U∩V=ℚ##." Homework EquationsThe Attempt at a Solution I only knew how to prove the first part. That is: (1) "Suppose that ##ℚ⊄U∩V##. This...

Homework Statement The surfaces ##x^2+y^2 = 2## and ##y=z## intersect in a curve ##C##. Find a unit tangent vector to the curve ##C## at the point ##(1,1,1)##. Homework EquationsThe Attempt at a Solution So I'm thinking that we can parametrize the surfaces to get a vector for the curve ##C##...

I'm having trouble even beginning to figure out how to approach solutions for this. I begin with a unit cube, and imagine all the possible lines that intersect the cube. I am assuming there must be an average length of these intersections; I want to find that average length. Another way to...

Homework Statement Consider two vector spaces ##A=span\{(1,1,0),(0,2,0)\}## and ##B=\{(x,y,z)\in\mathbb{R}^3 s.t. x-y=0\}##. Find a basis of ##A\cap B##. I get the solution but I also inferred it without all the calculations. Is my reasoning correct Homework Equations linear dependence...

Homework Statement Suppose that ##H## and ##K## are subgroups of finite index in the (possibly infinite) group ##G## with ##|G : H|m## and ##|G:K|=n##. Prove that ##lcm(m,n) \le |G : H \cap K | < mn##. Homework EquationsThe Attempt at a Solution I was able to get the upper bound on ##|G : H...

Let A,B,C be three sets such that : A={x∈ ℤ / x=11k+8 , k∈ℤ} B={x∈ ℤ / x=4k , k∈ℤ} C={x∈ ℤ / x=11(4k+1) -3 , k∈ℤ } Prove A⋂B = C I started with this : Let x be an arbitrary element of A⋂B then ∃(k,k')∈ ℤ² such that x=11k+8 and x=4k' then 11k+8 = 4k' then 11(k+1)-3 = 4k' I don't know where...

Homework Statement The exercise gives me ##V = <(1, 0, 0, 1), (-7, 0, 1, 0)>## and ##U = <(0, 4, 1, -1), (1, 12, 0, 26)>## and I have to find dimension and a base of ##V \cap U## and ##V + U##. Homework EquationsThe Attempt at a Solution They both have dimension ##2##. I find a vector ##\vec v...

Homework Statement ##W_1 = \{(a_1, a_2, a_3) \in \mathbb{R}^3 : a_1 = 3a_3,~ a_3 = -a_2 \}## ##W_2 = \{(a_1, a_2, a_3) \in \mathbb{R}^3 : 2a_1 - 7a_2 + a_3 = 0 \}## Given that these are two subspaces of ##\mathbb{R}^3##, describe the intersection of the two, i.e. ##W_1 \cap W_2## and show that...

Homework Statement Given two planes, P1, P2. Find parametric equations for the line of intersection between the two planes. Homework Equations P1 = 2x -3y + 4z = 3 P2 = x + 4y - 2z = 7 The Attempt at a Solution Let N1 be the normal vector to P1, and N2 be the normal vector to P2. Then, N1...

Will the bivariate function ##f(x,a)## always intersect ##f(a,x)## at the point ##x=a## given that ##f## is a real, defined function? (other points of intersection can exist but are not relevant for this question)

Homework Statement I have this exercise that tells me to determine a base and the dimension of the subspaces of ##\mathbb {R}^4##, ##U \cap Ker(f)## and ##U + Ker(f)##, knowing that: ##U = <\begin{pmatrix} -10 \\ 11 \\ 2 \\ 9 \end{pmatrix} \begin{pmatrix} 1 \\ 1 \\ 1 \\ 3 \end{pmatrix}...

I am a little confused here: a) The number 2 which is at the beginng of one set is closed. The number 2 is open at the beginning of the other set. b) The number 2 is closed of the beginning of a set which goes to infinity. The other set begins at 0 and goes to infinity (2 is an...

What is the angle of intersection between the two planes in ℝ3 with general equations x-y=5 and y-z=7? I know that the angle between then is equal to cos-1 (u⋅v/||u|| ||v||) but I am stuck on the general equations given, how can I solve when given these ?

Re: Union and Intersection of Sets Hi, Please I need a help regarding Union of sets can anybody solve this A={1,2,3} and B={{1,2},3} then what is A Union B and A Intersect B Thanks

Hello all, I am interested in both physics and applied math. One of my professors is willing to work with me to get into a great applied math school, but I don't want to abandon my passion for physics. Is there work being done at the intersection of applied math and physics? Is it reasonable...

Hi, I am reading "mathematical analysis" by Apostol right now for a course in analysis. Since I am trying to understand the author's proof of the above theorem(3.25 in the book), but I have something that I can't understand. He assumes that each of the nested sets contains infinitely many...

Hey! :o I want to show that if $S\in \text{Syl}_p(G)$ and $N\trianglelefteq G$, then $N\cap S\in \text{Syl}_p(N)$. Could you give me some hints how we could show that? (Wondering) Do we maybe use Frattini's Argument? (Wondering) From that we have that since $N\trianglelefteq G$ and $S\in...

My professor did this exercise that I didn't quite get how she went through all of it. We have a ##U = {(x, y, z, t) : x+y+z+t = 0}## and ##B_{Im(f)} = \left[ \begin{pmatrix} 7 \\ -3 \\ 0 \\ 0 \end{pmatrix}, \begin{pmatrix} 3 \\ -3 \\ 0 \\ 0 \end{pmatrix}, \begin{pmatrix} 5 \\ 0 \\ 1 \\ -5...

Hello! (Wave) Suppose that a parallelogram $ABCD$ has vertices $A=(0,0)$ and $B=(1,0)$. In terms of $C=(x,y)$, find the position of $D$ and where the two diagonals will intersect. Then we will have something like that: How can we find the coordinates of $M$, i.e. the point at which the two...

I was working on a problem on this domain: E=[x,y,z)\:s.t. \: \sqrt{x^2+y^2}\leq z\leq \sqrt{3x^2+3y^2},\: x^2+y^2+z^2\leq 2] and at some point I wanted to find the intersection of the internal cone(##\sqrt{3x^2+3y^2}=z##) with the sphere of radius ##\sqrt{2}## to find the height z of the...

How can I find the line of intersection between the planes 2x-y+2x+1=0 and -4x+2y-4x-2=0 I realize these are parallel as they are multiples of each other, but I'm not sure how to solve for the point. I also have to convert this line into parametric, cartesian and vector form. Sorry for the...