Intersection Definition and 688 Threads

Homework Statement Suppose that a group G has a subgroup of order n. Prove that the intersection of all subgroups of G of order n is a normal subgroup of G. Homework Equations The Attempt at a Solution I know that I need to do the following: Let S be the set of all subgroups of...

Homework Statement Show that the following pairs of lines intersect. Determine the coordinates of the point of intersection. L1: r= (-3,-1) + t(3,4) L2: r= (6,2) + s(3,-2) Homework Equations ? The Attempt at a Solution I know that eventually the two lines will reach the...

Homework Statement Find the parametric equations of the line tangent to the curve of intersection of the paraboloid z = x² + y² and the ellipsoid 4x² + y² + z² = 9 at the point ( -1, 1, 2 ). Homework Equations Probable use of the gradient vector (as this is the chapter we are in)...

Homework Statement I have to find all of the points of intersection of the curves... r2 = sin(2θ) r2 = cos(2θ) The Attempt at a Solution sin(2θ) = cos(2θ) 2sinθcosθ = cos2θ - sin2θ 2sinθcosθ - cos2θ = -sin2θ cosθ(2sinθ - cosθ) = -sin2θ This is where I'm having a problem, I'm...

Homework Statement Given a common intersection point (3,4,5), find 3 different planes. Homework Equations None The Attempt at a Solution What I did is let a1x+a2y+a3z=a b1x+b2y+b3z=b c1x+c2y+c3z=c 3=Dx/D 4=Dy/D 5=Dz/D I set D=2, therefore Dx=6 Dy=8 Dz=10...

Homework Statement I have to find the area of the region that lies inside the curves: r = sin(θ) r = sin(2θ) The Attempt at a Solution I'm assuming the first step would be to find the points of intersection so I know WHERE to integrate from/to, so I set the equations equal to each...

Homework Statement Find the centre of circle X2 + y2 + 4x – 16y + 18 = 0, show it's radius is 5√2 and find the co-ordinates where it is intersected by y = 3x - 6 Homework Equations The Attempt at a Solution X2 + y2 + 4x – 16y + 18 = 0 by completing the square using X2 + 2px = (x...

Homework Statement Find the point of intersection of two lines x = -9 + 5t y = 1 + t z = 10 - 4t and x = -2 -3t y = 5 + 2t z = 5 + 3t Homework Equations N/A The Attempt at a Solution I have read that you should set two of the equations equal to find the value of t, and...

Homework Statement |2x-1|+|x+2|\geq 4x Homework Equations The Attempt at a Solution For x<-2 , -(2x-1)-(x+2)\geq 4x x\leq -\frac{1}{7} For x\geq \frac{1}{2} 2x-1+x+2\geq 4x x\leq 1 For -2 \leq x < \frac{1}{2} , -(2x-1)+x+2\geq 4x x\leq \frac{3}{5} after...

Homework Statement Prove true: For any subspaces U,V of R^n dim(U intersect V) <= min(dim(U), dim(V)) Homework Equations Min(a,b) = the minimum value of A and B The Attempt at a Solution I know this statement is true however I can't quite figure out where to start on how to...

So for my homework I have to prove (or disprove) this statement: If U, V are two subspaces of Rn then U \cap V \neq \phi. I just want to make sure; \phi is the null set right? The set with nothing in it?

Homework Statement Find the parametric equation for a line of intersection of these two planes x+2y+3z=0 4x+5y+6z=5 Homework Equations Normal to plane 1= <1,2,3> Normal to plane 2= <4,5,6> The Attempt at a Solution I know the way to do this problem is to take cross product of...

Homework Statement Suppose L, M, and N are subspaces of a vector space. (a) Show that the equation L \cap (M+N) = (L \cap M)+(L \cap N) is not necessarily true. (b) Prove that L \cap (M+(L \cap N))=(L \cap M) + (L \cap N) Homework Equations N/A The Attempt at a Solution...

A couple of months ago I was pulled over by a police officer for running a stop sign. The officer claimed I "plowed right through" the stop sign. I honestly had no idea what he was talking about but wasn't about to argue with a cop. I realized after going back to check the intersection after...

L1: r(t) = (-5 + 2t)i + (5 + t)j L2: r(t) = (3 + 4t)i + (4 - 8t)j I know that they are perfendicular but how do I go about finding the point of intersection?

Homework Statement The starting position of a particle in R3 is (1,1,1) and it's traveling with constant velocity (2,-1,1). Where does it hit the plane {(x,y,z)|x - 2y + z = 4}. And find the angle between the path of the particle and the plane. Homework EquationsThe Attempt at a Solution

Hi everybody! I have a question, if I have A and B simply connected subspaces of a geodesic space X, what can be said about their intersection? When is it simply connected? Are there rules for this? I need to prove it in a special case, but I am not able to do it and I was wondering if...

Homework Statement Consider the intersection between the following two planes given in parametric form: P1 : x = [2, 4. 3] + s1[1, 2, 1] + s2[2, 5, 4] P2 : x = [1, 0, -5] + t1[3, 8, 7] + t2[2, 1, -5] Find the intersection of the two planes as a line in parametric form. Homework...

Homework Statement Find the point of intersection Homework Equations Equation 1 y=1/5(2)4x-7 Equation 2 y=1/10(1/2)9-3x The Attempt at a Solution Made them equal each other got rid of the 1/5 one one side and it made the 1/10 turn into 1/2 and now i don't know...

Homework Statement prove that (U\bigcapW)^{\circ}=W^{\circ}+U^{\circ} First prove That (U\bigcapW)^{\circ}\supseteqW^{\circ}+U^{\circ} Take any f\in (U\bigcap W)^{\circ} Then it is easy to see that for any f\in (U\bigcap W) f(v) =0 but since v\in U and v \in W then f \in...

Hey Guys. I have some questions about vector spaces, I would really apreciate if somone could read this and let me know if I understand things or not, and if not let me know where I have it wrong. I am having a lot of trouble UNDERSTANDING how to find the intersection of two vector spaced...

Consider the intersection of the sphere (x-3)^2+(y+2)^2+(z-1)^2=13 with the plane x+y=0 a) This intersection should be a familiar curve. Describe the curve. b) Substituing x=-y or y=-x into the equation of the sphere does not give this curve. Explain the difference. I know that the...

Homework Statement y=x-x^3 y=0 Must find intersection points by way of the x-axis Homework Equations The Attempt at a Solution I know you have to set them equal to each other i just do not know what to do from there.

Homework Statement f(x) = 2x2-5x-12 is given; part a: find derivative of f(x) using first principles, part b: find the rate of change of f(x) at x=1, part c: the points at which the line through (1, -15) with slope m cuts the graph of f(x), part d: the value of m such that the points of...

Is it correct that the angle of intersection of two curves is the same in x,y coordinates as in r,theta coordinates? If so, why is this?

Homework Statement Find an equation of the plane that passes through the point (-1,2,1) and contains the line of intersection of the planes x + y - z = 2 and 2x - y + 3z = 1 Homework Equations Equation of a plane: a(x-x0) + b(y-y0) + c(z-z0) = 0 The Attempt at a Solution n1 =...

Here's a math problem that's giving me a head ache (though to some of you it might seem to be quite trivial) r,s\in N^\ast , r+1\leq s ; |A_i|=r, \forall i\in \{1,2,...,s\} the intersection of any r+1 of sets A_i is nonempty [1] prove that \bigcap_{i=1,s} A_i \neq \emptyset [C]...

the graph of y=kx+3 intersects the graph of y=x^2 +8x at two distinct points for 'k 'equals what? to be honest I do not know where to start

Homework Statement Find the tangent vector at the point (1, 1, 2) to the curve of intersection of the surfaces z = x2 + y2 and z = x + y. Homework Equations The Attempt at a Solution I haven't started the problem, because I'm not sure what the first thing to do is. Do I have to parametrize...

How do I find this?

Homework Statement Let E and F be two subspaces of R^n. Prove the following statements: (n means "intersection") If EnF = {0}, {u1, u2, ..., uk} is a linearly independent set of vectors of E and {v1, v2,...vk} is a linearly independent set of vectors Note: Above zero denotes the...

hi everyone ! we have two circles that doesn't have intersections now we want to find a point on each circle that the distance of this two points are 'k' please help me . . .

If two spheres of radius 1 intersect each other so the surface of each sphere passes through the other’s center how could you find the exact volume of the intersection? It doesn't matter what kind of method, it could be double or triple integration, geometry, polar, cylindrical or spherical...

Homework Statement L1 passes through (1,-4,0) and (9,0,4) L2 passes through (2,-3,-1) and (4,-3,3) Do L1 and L2 intersect? If so, where? Homework Equations Parametric equations(?) The Attempt at a Solution A = (1,-4,0) B = (9,0,4) C = (2,-3,-1) D = (4,-3,3) AB =...

Homework Statement x1t= 2-cos(pi*t) y1t= 3+7sin(pi*t) x2t= 3t+2 y2t= -(7/15)(3t+1)2 + 157/15 Find points of intersection and collision Homework Equations above? The Attempt at a Solution Well, to find the intersection I think I need to eliminate the parameters for both...

Hello, I need help with this problem: A: 67,000 Purchasing managers that are male B: 33,000 purchasing managers that are female C: 245,000 financial managers that are male D: 150,000 financial managers that are female Out of these 495.000 individuals , what is the probability that a...

Hi I need some support regarding a problem. I know the poistion of a point in 3D let say (sp,yp,zp) and I know the circle with Center (xc,yc,zc) having radius rc. My question is how to find the intersection point of the circle and a line in 3D. I know that we can find the POI in 2 D by...

Homework Statement Find simpler notation for the two sets: A= \bigcup^{\infty}_{j=0}[j,j+1] and B= \bigcap_{j \in Z}(R minus\ (j,j+1)) Homework Equations The Attempt at a Solution Not really sure what it means by "simpler notation"... Does A=R since the union of...

Hi all, I'm quite new here, but it's been a while since I've been browsing through these forums for past answered questions for calculus and physics, but now comes the time where I'm the one needing help that's not been questioned yet. Homework Statement Find some* vector funcion r with...

I'm having a hard time creating a tidy equation to solve this seemingly simple problem. I have two points in standard 3D cordinate space, we'll call them C and D to be consistent with my work. The location of these points is given by (Ci,Cj,Ck) and (Di,Dj,Dk). I then have a third point, A...

Homework Statement H and K are subgroups of G. Prove that H\capK is also a subgroup. The Attempt at a Solution For H and K to be subgroups, they both must contain G's identity. Therefore, e \in H\capK. Therefore, H\capK is, at least, a trivial subgroup of G. This was a test...

Homework Statement The plane 4x − 3y + 8z = 5 intersects the cone z^2 = x^2 + y^2 in an ellipse. Use LaGrange Multipliers to find the highest and lowest points on the ellipse. Homework Equations Lagrange Multiplier The Attempt at a Solution I guess I lack an understanding of...

Show that the circle that is in the intersection of the plane x+y+z=0 and the sphere x2+y2+z2=1 can be expressed as: x(\vartheta) = (cos(\vartheta)-(3)1/2sin(\vartheta)) / (61/2)y(\vartheta) = (cos(\vartheta)+(3)1/2sin(\vartheta)) / (61/2)z(\vartheta) = -(2cos(\vartheta)) / (61/2) I'm really...

Homework Statement Generalize to obtain (C1 U C2 U...U Ck)' = C1' intersect C2' intersect...intersect Ck' ' = complement Say that C1, C2,...,Ck are independent events that have respective probabilities p1, p2, ..., pk. Argue that the probability of at least one of C1, C2,...,Ck is equal to 1...

Homework Statement For a any parabola with the equation y=kx^{2} I'm trying to find a curve that intersect every point of the parabola at right angles. Homework Equations For a perpendicular intersection the slope is -\frac{1}{m}The Attempt at a Solution I took the derivative and then took...

Homework Statement Find the point(s) of intersection (if any) of the plane and the line. Also determine whether the line lies in the plane. 2x-2y+z=12, x-\frac{1}{2}=-y-\frac{3}{2}=\frac{x+1}{2} Homework Equations 2x-2y+z=12 x-\frac{1}{2}=-y-\frac{3}{2}=\frac{x+1}{2} The...

I don't quite understand the meaning of "infinite union" and "infinite intersection". Is an infinite union ∞ U Ak k=1 being defined as a limit lim (A1 U A2 U ... U An) ? n->∞ How about an infinite intersection? Thanks!

I've two problems: Given are the two sets A = \left \lbrace (x_{0}, x_{1}, x_{2}, x_{3}) \in \mathbb{R}^{4} \mid x_{0}^{2} = \vec{x} \, ^{2}, x_{0} \geq 0 \right \rbrace and B = \left \lbrace (x_{0}, x_{1}, x_{2}, x_{3}) \in \mathbb{R}^{4} \mid (k_{0} - x_{0})^{2} = (\vec{k} -...

Homework Statement Find the plane that passes through the point (-1,2,1) and contains the line of intersection of the planes: x+y+z=2 2x-y+3z=1 The Attempt at a Solution First, I know that I need to find the line of intersection of the 2 planes. To do this, I used the cross product...

Homework Statement There is only a small issue that i am confused about... If we have a set \left(-\frac{1}{n},\frac{1}{n}\right), where n is a natural number. If we want to find the intersection of all such sets, my question is whether the result will be the set containing only...