Intersection Definition and 688 Threads

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 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...

Intersection of 3 Lines in Space Homework Statement L0 contains point P(1,0,2) and it meets L1: x=y=z+2 L2: x+3=-y/2=z/3 Find equation of Line L0. The Attempt at a Solution So we know that l1 and l2 are skewed. Based on the given info: L1) x=t...

If I is empty, and the collection of sets {A_i} is indexed by I, then the intersection of all the A_i is equal to the universal set. Can someone explain why? Or better yet, give a proof?

[SOLVED] trouble finding curve intersection Homework Statement Sketch the area of the region bounded by the curves y^2+4x=0 and y=2x+4. Set up two integrals, one with respect to x and one with respect to y, for finding the area of the region. Evaluate one of the integrals to find the area...

Homework Statement Hi there, Two points on the sphere S of radius 1 have spherical coordinates P: \phi = 0.35 \pi, \theta = 0.8 \pi and Q: \phi = 0.7 \pi, \theta = 0.75 \pi. Find a vector parallel to the line of intersection of the tangent planes to S at the points P and Q. 2. The...

Homework Statement Prove (A is a union of B)/(A is an intersection of B)=(A/B) is a union of (B/A) Homework Equations The Attempt at a Solution Could someone first help me translate all of this into plain English. I don't really understand what I need to prove. Would I start off...

Homework Statement Prove A intersects B=empty set if and only if B is a subset of (X/A) Homework Equations The Attempt at a Solution Would I prove the contrapositive in this case? If B is not a subset of (X/A), then the intersection of A at B is not the empty set Could...

Homework Statement True or False: The intersection of two planes in R3 is always a line. The Attempt at a Solution I'm pretty sure that this statement is true because two planes can only be parallel, or they must intersect in a line because the are infinate. But I have no ideas on...

Determine the curve of intersection of the surfaces x^2 + y^2 + z^2 = 4 and x + y + z = 1. The curve should be in parametric form. With this problem, I'm really not sure what direction to go in. I had thought about using the quadratic formula in some manner, but really unclear. Any advice...

Given the parametric representation of two planes, through points P and Q respectively x = P + \alpha u + \beta v y = Q + a w + b z Or, alternately, with u \wedge v = A, and w \wedge z = B x \wedge A = P \wedge A y \wedge B = Q \wedge B It's easy enough to find...

[SOLVED] Parametric equation of the intersection between surfaces Homework Statement Given the following surfaces: S: z = x^2 + y^2 T: z = 1 - y^2 Find a parametric equation of the curve representing the intersection of S and T. Homework Equations N/A The Attempt at a Solution The...

[SOLVED] Union and Intersection of sets Homework Statement a) Find: \bigcup_{i=1}^{\infty}} A_i b) Find: \bigcap_{i=1}^{\infty}} A_i Where A_i = (0,i), that is, the set of real numbers x with 0 < x < i I was doing okay when they gave me A_i = {i, i+1, i+2, ...}, but now that...

Homework Statement a) Find: \bigcup_{i=1}^{\infty}} A_ib) Find: \bigcap_{i=1}^{\infty}} A_i Where A_i = (0,i), that is, the set of real numbers x with 0 < x < i I was doing okay when they gave me A_i = {i, i+1, i+2, ...}, but now that they're giving me (0,i), and introducing x, I'm getting...

I'm trying to prove \bigcap^{\infty}_{n=1}(0,1/n) = EMPTY SET. One thing that I can't seem to bypass is getting past the closed intervals as stated in the Nested Interval Property, which states "For each n\in N, assume we are given a closed interval I_n = [a_n, b_n] = {x \in R : a_n \leq x...

The question asks that I : Find the point of intersection for each pair of lines. a) x + y= 4, x - 2y=1 b) x + 2y= 0, x - y= 3 c) 2x + y= 1, x + y= 2 d) 6x= 12 - 3y, 1/2y - x= -5 e) 1/2x - y=8, x + 1/3y= 2 f) 5 + y= 4x, x + 2= 2/3y I understand the formula of y=mx+b, m being the...

You are driving to the grocery store at 20 m/s. You are 110m from an intersection when the traffic light turns red. Assume that your reaction time is 0.50s and that your car brakes with constant acceleration. How far are you from the intersection when you begin to apply the brakes? What...

Hi, everyone: I am trying to understand the intersection form, and I am having trouble with the notation used in Wikipedia's entry on intersection theory: http://en.wikipedia.org/wiki/Intersection_theory_%28mathematics%29 Now, I am somewhat weak in my cohomology, and I...

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

Ive got a function of f(x)=x^3+x and I need to use factors to show that the graph crosses the x-axis once only. I just factorised it to x(x^2+1) which isn't very helpful, and if i divide everything by x and complete the square with x^2+1 i get a negative number and stuff... any help?

Homework Statement Show that the intersection of any two subrings of a ring is a subring. The Attempt at a Solution It seems abstract. suppose a+b=c and a*b=d Then if c is in A and B (where A and B are subrings) then the intersection of A and B denoted by C contains c and if C...

z=x^2+y^2 and x^2+y^2+z^2=2...I need to find the intersection of these two surfaces. Would I just substitute z=x^2+y^2 into the equation of the sphere to find the curve of intersection? But when I do that I get an equation with fourth powers and I don't know what kind of curve that makes.

Homework Statement I am asked to find the curve of intersection between x^2 + y^2 + z^2 = 36 and 2x + y -z = 2. Homework Equations The Attempt at a Solution I know the first equation is a sphere of radius 6, and the second equation will pass through it, so when projected on the xy...

I'm trying to find where x+y=1 meets x=2(y^2) To solve for y I set up: 2(y^2)=1-y 2(y^2)+y=1 y(2y+1)=1 I have y=1 and 2y+1=1 for 2y+1=1, 2y=0 so y=0 y=0,1 But, I notice that my teacher did: 2(y^2)+y-1=0 (2y+1)(y-1)=0 y=-1, 1/2 Why are these 2 methods bringing about different answers...

[SOLVED]Finding the point of intersection of two lines Hi, I would really, really appreciate it if someone could help me with this. Homework Statement Find the point of intersection between the lines: R_1(\lambda)=[1,\hspace {4} 0 \hspace {4} ,-1] + \lambda[1, \hspace {4} 1,\hspace {4} 1]...