Vectors Definition and 1000 Threads

Homework Statement Find the eigen values and normalized eigen vectors for the matrix cosθ sinθ -sinθ cosθ 2. The attempt at a solution Well I did the eigen values hope they are correct but can't solve for eigen vectors Eigen values are λ = cosθ ± isinθ on solving for eigen vector for...

<<Mentor note: Missing template due to originally being posted elsewhere>> Hello everyone. I have the following problem: Determine the angles of a triangle where two sides of a triangle are formed by the vectors A = 3i -4j -k and B=4i -j + 3k I thought that I would find the third side being...

I've been asked by someone with minimal background in physics to explain what vector and scalar quantities are and give examples. Here are my thoughts: A scalar is a quantity that has a magnitude only, it is completely specified by a single number. Importantly, it has no directional dependence...

Hi. I'm trying to understand tensors and I've come across this problem: "Show that, in general, a (2, 0) tensor can't be written as a tensor product of two vectors". Well, prior to that sentence, I would have thought it could... Why not?

I was watching a video explaining Einsteins field equations for beginners and he was giving some information on Vectors before he gets into the actual equations. He got to this equation: I'm real confused, how does he know that dx and dø are both? Why does dø change to dy? What does the...

I know that projection of vector B on A is ||B||cos(theta) where theta is the angle between vector A and B . But why do we find it . Is there any application for this

why addition of two vectors are represented by this diagram, why the sum of two vectors are between both the vectors. Does it takes the idea of hitting a ball , if we hit a ball to its left side it goes right side and when hitted to its right side it goes left side and when we hit...

Homework Statement Charge q1 = +8.36 μC is fixed at the origin and charge q2 = -4.28μC is fixed on the +x-axis, 0.371m from the origin. (a) Find the direction and magnitude of the electric field at a point P that has coordinates (0.466, 0.466) m. (b) Find the direction and magnitude of the...

Hi. I have read that when working in 3-D the following kets | x > and | p > are not vectors in 3-D. If that is correct what are they ? I know | ψ > is an abstract vector but I thought | x > and | p > would be 3-D vectors in the position and momentum representation ? Thanks

Homework Statement ##r(t)=(t^2)i+(1+\frac{1}{3}t^3)j+(t-\frac{1}{3}t^3)k## Find the tangential, normal, and binormal vectors for this TNB frame. Homework Equations ##T(t)=\frac{v(t)}{|v(t)|}## ##N(t)=\frac{T`(t)}{|T`(t)|}## ##B(t)=T(t)×N(t)## The Attempt at a Solution The problem isn't that I...

Homework Statement The portable reel is used to wind up and store an air hose. The tension in the hose is 100 N and a vertical 200-N force is applied to the handle in order to steady the reel frame. Determine the minimum force P which must be applied perpendicular to the handle DE and the...

Find a set of vectors {u, v} in $\mathbb{R}^4$ that spans the solution set of the equations: $x - y + 2z - 2w = 0$ $2x + 2y -z + 3w = 0$ ($u$ and $v$ are both $4 \times 1$) $u = ?$, $v = ?$ I put the matrix in RREF to get $\begin{bmatrix}1&0&3/4&-1/4\\0&1&-5/4&7/4\end{bmatrix} =...

How is Δθ in circle equals to angle in velocity vectors triangle? I tried using simple geometry but I can't.

The problem: By considering w x (p x w) resolve vector p into a component parallel to a given vector w and a component perpendicular to a given vector w. Hint: a x (b x c) = b(a x c) - c(a x b) I'm afraid I really have no idea where to go with this one. The hint leads to: p(w.w) - w(w.p) =...

This is the problem: Suppose a, b and c are linearly independent vectors. Determine whether or not the vectors (a + b), (a - b), and (a - 2b + c) are linearly independent. Here was my solution, which involved writing words (and hasn't actually been confirmed correct yet): Let's align a, b and...

how is flux scalar if the magnetic field and area both are vector quantities?

Question: Solution: The notation used is: ##(x,y,z)## is for rectangular coordinates, ##(\rho,\varphi,z)## for cylindrical coordinates and ##(r,\theta,\varphi)## for spherical coordinates. ##{ { \hat { a } } }_{ ρ }## represents the unit vector for ##\rho## (same applies to ##x, y, z##...

Homework Statement http://imgur.com/a/Yq8pWHomework Equations projection u onto v: ((u x v)/(||v||^2)) x v Unit vector: u/||u|| The Attempt at a Solution For number 2, I absolutely do not know how to set up the problem. I do not know what vectors to use, I assumed F vector to be <0.00375...

If we use n linearly independent vectors x1,x2...xn to form a vector space V and use another set of n linearly independent vectors y1,y2...yn to form a vector space S, is it necessary that V and S are the same? Why? If we have a vector space Q that the dimension is n, can we say that any set of...

The unit right now is electrostatics, but this question is really just vectors, nothing to do with charges or anything... anyways here is the info: 1. Homework Statement Three identical point charges, A, B, and C are located as shown here: The force A-on-C is the same as the force B-on-C...

Homework Statement Use the graphical and trigonometic solutions to calculate the total muscle force vector from thefollowing three quadriceps muscles i) rectus femoris pulling 75 N at 5°laterally from the vertical, ii)vastus lateralis pulling 50 N at 30°laterally from the vertical, and iii)...

consider the two vectors v1 = (3i, 2), v2 = (-3, 2i). in C^2 Above C we get, v1 * i = v2, therefore they are dependent. Now above R, we can't see that they are dependent. Why if i take the determinant of those vectors i get get 0 |v1 v2| = 2x2 matrix = 0 ( which means two column vectors are...

Homework Statement Homework EquationsThe Attempt at a Solution I can't remember what this method of calculation this is as it's been a while since I've done this. [/B] Could someone explain to me what I've done wrong in my calculations? The answer was 13.8N at 80 degrees.

Hello I found a bug in my code and can't figuring out the error. I tried debugging by showing the output of each variable step by step but I can't find my error. Here is what I have and what I want to do: I have a matrix A: 0000 0101 1010 1111 And I have a matrix B: 10000 21000 30100 41100...

Given a continuous random vector (X,Y) with a joint density function In order to check whether it is indeed a joint density ƒ(x,y) the method is to check if ∫∫ƒ(x,y)dxdy=1 where the integrals limits follow the bounds of x and y. However, is it the case that if given an arbitrary discrete random...

Suppose if I applied a 4N force and then 2N force on an object , what will be total force. Note I didn't said simoultaneously, I mean one after the other, then what will be the total force , I think 6N , i know about vector sum and etc.. but I think this question doesn't makes any sense...

Should not angle between vector P and Q be 180-θ rather than θ? According to my book it is θ.

(Scalar)·(Scalar) = Scalar (Scalar)·(Vector) = Scalar (Vector)·(Vector) = Scalar (Scalar)x(Scalar) = Not valid (Scalar)x(Vector) = Vector (Vector)x(Vector) = VectorDid I get them right, if not why? Thanks

Homework Statement Hi everybody! I might have solved that homework but I struggle to properly understand some steps, especially concerning the gradient and partial differentiation: The potential Φ(r) of an electric dipole located at the origin of a coordinate system is given by: \phi...

What is meant by taking the tensor product of vectors? Taking the tensor product of two tensors is straightforward, but I am currently reading a book where the author is talking about tensor product on tensors then in the next paragraph declares that tensors can then be constructed by taking...

I am having trouble finding the Cartesian equation of the line k which passes through Y(0,1,0) and is normal to -3x-2y+2z=0 this is what I tried to do but not sure if it is the correct method normal direction (-3,-2,2) -3x-2y+2z=d sub in (0,1,0) to -3x-2y+2z=d d=-2 -3x-2y+2z=-2 is...

How do I find the vector equation of the line which passes through (-3/2,-3/2,1/2) and is perpendicular to both x+1=y/3=-z and 2x+1=2y+1=z-5/2 I know how to do it using one equation but I am unsure about how to do it using two equations Thanks

Homework Statement In Euclidean three-space, let ##p## be the point with coordinates ##(x,y,z)=(1,0,-1)##. Consider the following curves that pass through ##p##: ##x^{i}(\lambda)=(\lambda , (\lambda -1)^{2}, -\lambda)## ##x^{i}(\mu)=(\text{cos}\ \mu , \text{sin}\ \mu , \mu - 1)##...

Neglecting equatorial bulge and using 'g' (9.81m/s^2) as standard before calculations, I wanted to see if I could calculate the change in 'g' before looking it up. Obviously this not a difficult sort of problem but I am finding myself a tad confused about something. It seemed intuitive to me...

If one has two single-particle Hilbert spaces ##\mathcal{H}_{1}## and ##\mathcal{H}_{2}##, such that their tensor product ##\mathcal{H}_{1}\otimes\mathcal{H}_{2}## yields a two-particle Hilbert space in which the state vectors are defined as $$\lvert\psi ,\phi\rangle...

I'm currently writing a test where my students will need to add two vectors using head-to-tail addition. I don't know how to draw vectors in LaTeX and the guides I've found have been quite tedious. I also considered doing it in Microsoft Paint, but it looks terrible. Any ideas on what software...

Homework Statement I was reading about the Hermite integration scheme for N-body simulations, as seen here: http://www.artcompsci.org/kali/vol/two_body_problem_2/ch11.html#rdocsect76 This scheme uses jerk, the time rate of change of acceleration. The problem is that I don't know how to...

My professor states that "A matrix is diagonalizable if and only if the sum of the geometric multiplicities of the eigen values equals the size of the matrix". I have to prove this and proofs are my biggest weakness; but, I understand that geometric multiplicites means the dimensions of the...

Why is ##a_{ji}dG_j'=dG_i'## ? from the third last line below. ##G_i=a_{ji}G_j'## because a vector labelled by the space axes is related to the same vector labelled by the body axes via a rotation transformation. If ##a_{ji}dG_j'=dG_i'##, then we are saying a vector ##dG'## labelled by the...

Homework Statement [/B] Find all algebraic vectors of $$R^2$$ r (r is a vector) such that $$\frac{\mathbf{r}}{\lvert\lvert \mathbf{r}\rvert\rvert} = (\frac{1}{2}\sqrt{2}, \frac{1}{2}\sqrt{2})$$ Homework Equations I don't think there is any equation related to this.. The Attempt at a Solution...

I'm sure this is a simple concept but i just can't wrap my brain around it, the question is: a) Express the following vectors in terms of x-y coordinates: i)Vector V with direction π/6 and magnitude 4√3. ii) Vector W with direction 5π/4 and magnitude 4√2. b) Express the vector v + w in terms...

Homework Statement Let A be an n x n matrix, and let v, w ∈ ℂn. Prove that Av ⋅ w = v ⋅ A†w Homework Equations † = conjugate transpose ⋅ = dot product * = conjugate T = transpose (AB)-1 = B-1A-1 (AB)-1 = BTAT (AB)* = A*B* A† = (AT)* Definitions of Unitary and Hermitian Matrices Complex Mod...

So I was trying to learn how to find the angle between two complex 4-dimentional vectors. I came across this paper, http://arxiv.org/pdf/math/9904077.pdf which I found to be a little confusing and as a result not overly helpful. I was wondering if anyone could help at all? Many thanks in...

I have a function of a 3 vector, i.e. f(+x,+y,+z) [ or for conveniance f=+++] this function is repeated 4 times where: f1 = + + + f2 = + - + f3 = - - + f4 = - + + I need a formula where i have a different vector for each function in a summation, to obtain the superposition of all 4...

Steven Weinberg has made what he calls a "modest proposal": http://arxiv.org/abs/1405.3483 Quantum Mechanics Without State Vectors Steven Weinberg (Submitted on 14 May 2014) It is proposed to give up the description of physical states in terms of ensembles of state vectors with various...

Homework Statement Homework Equations The Right-Hand Rule The Attempt at a Solution I'm having some issues with the right-hand rule to find the direction of magnetic force, and I'm doing a homework problem. The answers I got are (letters are vector directions): A: -j B: i C: j D: i E:-i...

Homework Statement [/B] Hi all, these were two even numbered exercises in my C++ textbook. I am self teaching the language so I am trying to get some of the basics down. 1. Would the following snippet of code best be described as an example of Polymorphism or Inheritance? class Shape {...

Homework Statement Find the equation of all planes containing the points P(2, -1, 1) and Q(1, 0, 0) Homework EquationsThe Attempt at a Solution I use PQ to get a vector, (-1, -1, 1). I some how need to use another vector so I can use the cross product to find the planes. So i let another...

I would like some help or guide to if i am going on the right track on my program ***Set numMatches to the number of elements in userValues (having NUM_VALS elements) that equal matchValue. Ex: If matchValue = 2 and userValues = {2, 2, 1, 2}, then numMatches = 3. ***#include <iostream> #include...

Homework Statement Does the line through the point P(1, 2, 3) with direction vector d = (1, 2, -3) lie in the plane 2x+y-z=3? Homework EquationsThe Attempt at a Solution From the 2x+y-z i can get the vector (2, 1, -3) and the direction vector, their dot product does not equal zero. So, no it...