Vectors Definition and 1000 Threads

Homework Statement Standard pool balls have a mass of 0.17kg. Before a collision, ball A is at rest and ball B is traveling at 4.5 m/s [N]. After the collision, ball B is traveling at 1.6 m/s [N20E]. What is the velocity of ball A? Homework Equations pinitial = pfinal m1v1 + m2v2 = m1v1 + m2v2...

I am just being introduced to the notion of covectors. I see that the gradient of a scalar function is thought of as a covector. Q1) On another source I have read to think of contravariant vector field as a differential operator: Va \partial _a and to think of a covariant vector field as...

Homework Statement A 9 kg object is subjected to two forces, http://www.webassign.net/images/Farrowbolditalic.gif1 = 7 N i - 4 N j and [PLAIN][PLAIN]http://www.webassign.net/images/Farrowbolditalic.gif2 = 7 N i - 9 N j. The object is at rest at the origin at time t = 0. (a) What is the...

So i don't really understand why the change in momentum of a crystal involves a reciprocal lattice vector. Surely it is just the change in momentum due to the change in the number and frequency of the phonons before and after whatever event/scattering/collision takes place. Can somebody please...

I have two problems that I cannot seem to figure out. I already know the answers, but I want to know the process of how to complete them so I know for quizzes and tests. 1. Vector A is 3 units in length and points along the positive x-axis; vector B is 4 units in length and points along a...

Find the result force of the two forces. This problem seemed easy at first, but I think I'm confused as to how to find the coordinate angle (gamma) . For the ( i,j,k) components of F1, I got (300cos(30)i, 0j, 300sin(30)k) I don't understand the function of the 45 degree angle, either. What am...

Homework Statement For the following vectors 'u' and 'v', express 'u' as the sum u = p + n where 'p' is parallel to 'v' and 'n' is orthogonal to 'v' u = {-1, 2, 3} v = {2, 1, 1} Homework Equations Dot product Cross product The Attempt at a Solution First, I should say that I do not know how...

You’re hanging from a chinning bar, with your ;arms at right angles to each other. The magnitudes of the forces exerted by both your arms are the same, and together they exert just enough upward force to support your weight, 620 N. (a) Sketch the two force vectors for your arms, along with their...

Homework Statement A man is standing in his home , his position his facing direction and the position of the sweet dish are given ,if he faces the sweet dish , he eats it . Translating it into CS programming question : write a function -> bool IsManInFrontofDish( vector3& manPosition, vector3&...

please someone explain me the following expression for Cartesian unit vectors expressed by the cylindrical unit vectors: http://web.mit.edu/8.02t/www/materials/modules/ReviewB.pdf at page B-8 line B.2.4 i would like to know which steps led to it. thanks, Chen

[Q] Find the integral that represents the flux of the vector F = <x^2z, x^z, x^2z> through the surface S given by z = Ax + By + C for 0 <= x <= a and 0 <= y <= a, where A, B, C, and a are positive constants. From what I remember of the Flux. F dot n, where n is a a vector perpendicular to the...

So I have two parametrized equations for two different 3d curves: Rm(t) = (1.2*sin(2πt) + 0:3)i + t4j + 1.1cos2(2π(t + 0:2))k and R(t) = Sin(2πt)i + t3j + Cos2(2πt)k I need to figure out if these two curves come within a certain distance of each other (0.5). I cannot understand how to find...

It is often stated that there are maximum number of n/2 (n+1) linearly independent killing vectors in an n-dimensional Riemannian manifold. How is this fact derived?

Homework Statement electric field polarization for a given antenna is expressed as: E_i = (a_x + a_y) E (r, theta, phi) The unit vector along the antenna polarization is found as u_a = 1/Sqrt(2) (a_x + a_y)2. Question Where/how is the 1/Sqrt(2) found to resolve those other 2 vectors into a...

if i have a vector field \vec{F}=(f_1,f_2,f_3),i know which for obtain 1-form associated with it i do \vec{F}^{\flat}=f_1dx^1+f_2dx^2+f_2dx^3, but how can i get the 2-form and p-form associated with that vector field? And one more thing, the musician isomorphisms which i used is only valid in...

Consider the three displacement vectors A with arrow = (-4i hat bold − 3j hat bold) m, B with arrow = (6i hat bold − 8j hat bold) m, and C with arrow = (-3i hat bold + 5j hat bold) m. Use the component method to determine the following. (a) The magnitude and direction of the vector D arrowbold...

I am working on a diff eq. that the prof. did as an example in class. ##y^{\prime\prime}-3y^{\prime}+2y=x^2+x+3## after subbing in I get: ##2a_2-6a_2x-3a_1+2a_2x^2+2a_1x+2a_o=x^2+x+3## She set aside the ##x^2## terms and set them equal to zero like such: ##2a_2x^2-x^2=0## I imagine this...

Hello, While studying dual vectors in general relativity, it was written as we all know that dual vectors (under Lorentz Transformation) transform as follows: \tilde{u}_{a} = \Lambda^{b}_{a}μ_{b} where \Lambda^{b}_{a}= η_{ac}L^{c}_{d}η^{db} I was wondering if one can prove the latter...

Homework Statement Suppose that you draw a point "x" in the middle of a page, and a curve going through "x" in such a way that the curve is going straight upward at the point "x" and is curving to the left. In what direction does the binormal vector "B" (at "x") point? Homework Equations None...

Homework Statement Suppose \mathbf{u,v,w} \in {\rm I\!R}^2 are noncollinear points, and let \mathbf{x} \in {\rm I\!R}^2. Show that we can write \mathbf{x} uniquely in the form \mathbf{x} = r\mathbf{u} + s\mathbf{v} + t\mathbf{w}, where r + s + t = 1. Homework Equations Suppose \mathbf{a,b}...

Homework Statement "Determine the design angle θ (0° ≤ θ ≤ 90°) for strut AB so that the 400-lb horizontal force has a component of 500lb directed from A towards C. What is the component of force acting along member AB? Take ϕ = 40°" Homework Equations x-component: magnitude*cos(θ)...

Homework Statement The figure below gives the path of a squirrel moving about on level ground, from point A (at time t = 0), to points B (at t = 6.00 min), C (at t = 12.0 min), and finally D (at t = 18.0 min). Both axes are marked in increments of 1.50 m (therefore the diagram is not drawn to...

Hi, I have two 1.5 lifting lugs supported in the roof of a concrete tunnel 3.5m apart at a height of 7m. The lugs require load testing and as per AS4991 require load testing to double the W.L.L therefore 3 tonne. My work has a 5 tonne RUD lug readily available therefore was thinking...

So I have an issue understanding how to compute a matrix using the Minkowski metric as a null (read light-like) spacetime vector. As best I can understand it, it is a vector which has all velocity in the spatial components and none in time. Also, would a vector that transcends the speed of...

Homework Statement The problem is worded thus: You are on an airplane traveling 30° south of due west at 130 m/s with respect to the air. The air is moving with a speed 30 m/s with respect to the ground due north. (a) What is the speed of the plane with respect to the...

Homework Statement Hello, I've been trying to solve this problem, but in the examples that my teacher gave me didn't include something like this, I know how to calculate area but only if I have all the coordinates established. I need to find the area using the cross product. Homework...

I've recently began a course on electromagnetism and have started dealing with complex vectors. I have a couple questions to ask: Regarding the general concept of complex vectors, I am curious what these actually represent. Refer to attached equation. Am I correct to believe that this...

Homework Statement A car is moving with speed ##17.4m/s## due south at one moment and ##28.3m/s## due east ##7.50s## later. A. Determine the magnitude and direction of its average velocity over this time interval. B. Determine the magnitude and direction of its average acceleration over...

Homework Statement An unsuspecting bird is coasting along in an easterly direction at 4.00 mph when a strong wind from the north imparts a constant acceleration of 0.300 m/s2. If the acceleration from the wind lasts for 3.50 s, find the magnitude, r, and direction, θ, of the bird\'s...

$r(t)=sin(t)$i $+ 2cos(t)$j $t= \pi/4$ sketch the position vector and the tangent vector $r'(t)=cos(t)$i $- 2sin(t)$j $r(\pi/4)= \frac{\sqrt{2}}{2}$i $+ \sqrt{2}$j $r'(\pi/4)= \frac{\sqrt{2}}{2}$i $- \sqrt{2}$j $\left\langle \frac{\sqrt{2}}{2}, \sqrt{2} \right\rangle$ $\left\langle...

Two vectors acting on a moving object that has a mass of 27kg.One force has a magnitude of 12 N and points due south, while the other force has a magnitude of 17N and points due west,find acceleration of the object? Calculate the resultant force acting on the object: RF² = 12² + 17² RF² =...

Homework Statement A and B are two unit vectors in the x-y plane. A = <cos(a), sin(a)> B = <cos(b), sin(b)> I need to derive the trig identity: sin(a-b) = sin(a) cos(b) - sin(b) cos (a) I'm told to do it using the properties of the cross product A x B Homework Equations A x B =...

Hi all, I was asked by someone today to explain the notion of linear independence of a set of vectors and I would just like to check that I explained it correctly. A set of vectors S is said to be linearly dependent if there exists distinct vectors \mathbf{v}_{1}, \ldots , \mathbf{v}_{m}...

I have a question on finding the counter clockwise angle the vector difference B-A makes with the +x axis I already have the components of vector difference for B-A and I have checked that they are correct they are 2.77,-5.95 I started with doing the tan function (opp/adj) which was -5.95/2.77 I...

Homework Statement Determine the vectors A-C, given the vectors A and C in Fig. 3-32. Vector A=44.0 at 28 degrees north of east and vector C=31.0 at 90 degrees south of east. Homework Equations I don't know any. The Attempt at a Solution 44.0-31.0=11.0, 28.0-90= -62 The answers...

[1] A car is driven 215 km west and then 85 km southwest. What is the displacement of the car from the point of origin (magnitude and direction)? Draw a diagram. [2] I have no idea what equations are necessary for this problem. I reread the chapter, but this problem in particular is stumping...

Let me say from the beginning I'm not talking about the non-coordinate unit vectors for polar coordinates. I'm talking about basis vectors. Let me just ask it as boldly as possible: how does one use these basis vectors in order to describe a vector? I know they are different at every point, so...

In Frankel's book he writes that in R^{3} with cartesian coordinates, you can always associate to a vector \vec{v} a 1-form v^{1}dx^{1}+v^{2}dx^{2}+v^{3}dx^{3} and a two form v^{1}dx^{2}\wedge dx^{3}+v^{2}dx^{3}\wedge dx^{1} +v^{3}dx^{1} \wedge dx^{2}, now in general this is not possible and you...

find $a+b, 2a+3b, \left| a \right|, \left| a-b \right|$ $a=\left\langle 5,-12 \right\rangle$ $b=\left\langle -3,-6 \right\rangle$ ive found all of them except the last one. how to do i find $\left| a-b \right|$

Homework Statement I've been stuck on this problem for hours. Any help you can provide is greatly appreciated. From a lookout point, a hiker sees a small lake ahead of her. In order to get around it, she walks 4.5km in a straight line toward the end of the lake. She turns right making...

Hey guys sorry if this isn't in the right place, I'm new to these forums. Just wondering if someone could clarify to me what N25°W means? Is it 25 degrees west of north? Thank you!

I am a little confused about how exactly vectors are used. For example, if we had the two statements \vec{r} = 3\hat{i}t + 4\hat{j}t and \vec{r} = \frac{1}{2}\vec{a}t^{2} + \vec{v_{o}}t + \vec{x_{o}} What is the difference between the two equations (assuming they are both true)? I...

Can we make curvy vectors? Or to put it another way: Instead of one straight direction, can the direction be round(or something like that)? Thanks

There are two "formal" definitions of vectors (and tensors in general) which I've learned. The first is what I consider the "better" definition, one I learned in linear algebra. We call a set X a vector space over a field F whenever that set has properly defined operations of scalar...

The problem I am having is a problem in my textbook. It says that if we have xy Cartesian coordinate system, and if we then have a rotated coordinate system x'y', then to get the vector in the x'y' in terms of the xy system, we use the following arguments for the unit vectors: i' = icos\Phi +...

Homework Statement Suppose \vec{u}, \vec{v} and \vec{w} are vectors in an inner product space such that: inner product: \vec{u},\vec{v}= 2 inner product: \vec{v},\vec{w}= -6 inner product: \vec{u},\vec{w}= -3 norm(\vec{u}) = 1 norm(\vec{v}) = 2 norm(\vec{w}) = 7 Compute...

Hi everybody, I apologize if this question is too basic but I did 1 hour of solid Google searching and couldn't find an answer and I'm stuck. I'm reading Bishop's Pattern Recognition and Machine Learning and in the second chapter he introduces partitioned vectors. Say, if X is a D-dimensional...

Hi! [FONT=HelveticaNeue]Ok, I got another question here. I don't understand how to draw the vectors. This is a method to simplify analysis of unbalanced three-phase power systems but I just don't understand the drawing here. Do you think you can explain how? I understand how to draw the vectors...

In a perfect periodic crystal, do lattice vibrational modes corresponding to different wave vectors (k-vectors) interact with each other? I'm asking with reference to anharmonic lattice-dynamics calculations of a time-independent nature. For example: consider a linear, monatomic chain with a...

Suppose T=T(r,θ)=G(x,y) How do you prove ∇T(r,θ)=∇G(x,y)? I can think of some arguments in favor of this equality, but I want an actual proof or a very good intuitive argument. My arguments in favor go something like this: -Gradient vectors should be the same because if my directional...