Vectors Definition and 1000 Threads

What exactly is all this 'matrix elements of vectors' stuff that Landau is talking about? I don't mean to ask people unfamiliar with this section to read it for me, so hopefully for someone who's read it - what's going on and where would I find a more modern discussion of this section (I'm...

Homework Statement In the previous few modules you studied the problem of minimizing ##\| Ax -b \|_{2}## by choice of ##x##. So far you've done this in Matlab using either the backslash operator or the command pinv. Now that you've been exposed to linear programming, you have the tools to solve...

Hi, Given several vectors, which may be or not be orthogonal to each other, how to construct a vector perpendicular to them? In a sense of inner production being zero. To be specific, I have n vectors v_{N} of length N, where n<N. So the maximum rank for these vectors is n, which leaves...

I understand that dot product of vectors means projecting one vector on to the other. But I don't understand what is the physical significance of a cross product? I have read that cross product gives the area of the parallelogram which has each of the vectors as its sides...but why do we want to...

During an interaction on TeX.SE, egreg there posted some truly awesome code for doing unit vectors in $\LaTeX$: \usepackage{newtxtext} \usepackage{newtxmath} \usepackage{amsmath} \usepackage{bm} \newcommand{\uveci}{{\bm{\hat{\textnormal{\bfseries\i}}}}}...

Hi everybody, I'm a physics student and this is my first post here and i will begin asking one favor: Anyone could recommend a simple and accessible book about vectors in linear algebra?? I'm already read several books and didn't understand anything.. :cry: I really need to recover my...

Homework Statement So I was wondering how do we account for vectors that are at a certain angle. The problem that I'm having with the picture is: if I was calculating torque from point B, how would I account for the vector G. Homework Equations The Attempt at a Solution I've...

Homework Statement A body is acted on by two forces. Find the magnitude and direction of the resultant force by using the mathematical method. I'm not sure if I've done this correctly, any pointers would be appreciated :) Also what is the angle between the two vectors? Is it 90 or 76 degrees...

Hi everyone, I have to find out how to do cross and dot product for two vectors in non-orthogonal coordinate system. thanks

How can a discrete time signal can be a vector? i cannot grasp the idea. i know MATLAB uses matrices which denote vectors, but how does a discrete time varying amplitudes be a vector?

Hey PF! I am trying to understand what is meant when we say a vector is invariant, which I believe is independent of a coordinate system. I have already read a PF post here: https://www.physicsforums.com/showthread.php?t=651863. I'm looking at DH's post, and this makes a lot of sense...

I was reading in my textbook that the scalar product of two complex vectors is also complex (I assuming this is true in general, but not in every case). However for the general definition (the inner product), each element of one of the vectors needs to be its complex conjugate. I learned this...

I want find a value M such that given v and u, satisfies the equation v=Mu. Well, the vector u has a modulus u and a direction α wrt x-axis; the vector v has another modulus v and another direction β wrt x-axis. What is happened is a change of magnitude and direction of the vector u...

Hi Guys, Im working on finding an angle between two vectors. a [ 1,2,3 ] b [ 4, -1, 0] //a// = sqrt(1^2+2^2+3^2) = sqrt14 //b// = sqrt(4^2+(-1)^2+0^2 = sqrt17 Dot product 1.4 + 2.-1 + 3.0 = 2 cos^-1 2/ sqrt14 sqrt17 cos^-1 (1/( ? ) Thanks

Hello and apologies if the title of the question is not very precise. Question: I am reading the document talking about the simulation of photons in tissues using a Monte Carlo simulation. The exact title is "MCNP - A general Monte Carlo N-Partcle Transport Code". Link to MCNP - A general...

Hey there, This isn't a homework question, it's for deeper understanding. So I'm learning about unit normal/tangent vectors and the curvature of a curve. I have a few questions/points. 1) So my book states that we can express acceleration as a linear combination of the acceleration in the...

If I define a state ket in the traditional way, Say: $$|\Psi \rangle =\sum _{ i }^{ }{ a_{ i }|\varphi _{ i }\rangle \quad } $$ Where $$a_i$$ is the probability amplitude. How does: $$\hat {H } |\Psi \rangle =E|\Psi \rangle $$ if the states of $$\Psi$$ could possibly represent states...

I am having trouble solving a basic problem in the use of vectors. The problem comes from Alonso & Finn "Fundamental University Physics" Volume 1, Chapter 3 Problem 12 and states "The pennant on the masthead of a sailboat streams back at an angle of 45 degrees (South of West), but the flag on...

Homework Statement If |v|=4, |w|=3 and the angle between and is pi/3, find |2v −w| Homework Equations ##cosθ=\frac {v dot w} {|v||w|} ##The Attempt at a Solution ## 6= v dot w ## This is as far as I got. How would I find the separate values of v and w for the equation?

I've made mistakes where scaling was used but I just assumed that I didn't need it. e.g. a bug walking towards <1,1,1> is scaled to <1/sqrt(3), etc>. Under what kind of conditions/in what kind of problems should vectors be scaled? I know that v/|v| is the unit vector but how do I relate this to...

Homework Statement For a set of vectors in R3, is the set of vectors all of whose coordinates are integers a subspace?The Attempt at a Solution I do not exactly understand if I should be looking for a violation or a universal proof. If x,y, z \in Z then x,y,z can be writted as...

I was looking at a homework question posted here requiring proof that the vectors from the vertices of a triangle to the midpoint of the opposite edge sum to zero, and it struck me that there is a more general property: Consider a set of points, \{A_0, A_1, \ldots A_n\}. The midpoint of...

Homework Statement A triangle has verticies A(-2,1,3), B(7,8,-4), and C(5,0,2). Determine the area of the triange ABC. The correct answer is 35.9 square units. Homework Equations Has to be done by using dot product and/or cross product. Dot product: a(dot) b= |a||b|cos(theta) Cross...

Homework Statement Two velocities acting at a particular point are such that: The sum of their respective magnitudes is 15m/s The product of their respective magnitudes are 56m2/s2 The resultant is 13m/s. Find the two velocities and the angle between them. Homework Equations R^2 = P^2 + Q^2...

Homework Statement A plane is given by the equation: 4x + 5y + 7z = 21 and a line by the equation r = (1,2,3) + \lambda (1,2,-2) where λ is real. Show that the line does not intersect the plane. The attempt at a solution So if I remember correctly, if n . a = 0 , they do not...

I have a unique problem that I'm struggling with with regards to surveying. Because my surveying equipment is much more accurate at measuring angles than distances I'd like to find an analytic solution using only the angular measurements. Let the surveyor sit at the origin of the...

Homework Statement Say we have the plane, x+2y+4z=8 (part of a larger problem) Homework Equations The Attempt at a Solution The vectors (8,0,0) and (0,0,2) both lie in the plane. They are linearly independent. But (0,4,0) lies in the plane and is not a linear combination of the first two...

Homework Statement A book of mass M = .55 kg rests on a table where the coefficient of static friction us = .45. A force, F = 4 N acts on the book at an angle of 15 degrees above the surface of the table. What is the acceleration of the book if the coefficient of kinetic friction uk = .23...

Can someone explain why the derivative with respect to a contravariant coordinate transforms as a covariant 4-vector and the derivative with respect to a covariant coordinate transforms as a contravariant 4-vector.

In "A Student's Guide to Vectors and Tensors" by Daniel Fleisch, I read that the covariant metric tensor gij=ei°ei (I'm leaving out the → s above the e's) where ei and ei are coordinate basis vectors and ° denotes the inner product, and similarly for the contravariant metric tensor using dual...

Here is a example 1.3 from analytical dynamics of Haim Baruh. a particle moves on a path on the xy plane defined by the curve y=3*x^2 , where x varies with the relation x= sin(a). find the radius of curvature of the path and unit vectors in the normal and tangential directions when a=pi/6...

Homework Statement This problem is from Mary Boas' "Mathematical Methods in the Physical Sciences" 3rd Ed. Capter 3 Section 4 Problem 3 Use vectors to prove the the following theorems from geometry: 3. The diagonals of a parallelogram bisect each other. Homework Equations Just...

Homework Statement In this question we consider the following six points in R3: A(0,10,3) B(4,18,5) C(1,1,1) D(1,0,1) E(0,1,3) F(2,6,2) a) Find a vector equation for the line through the points A and b b) Find general equations for the line from a c) Find a vector equation for the...

Homework Statement Vector J has a magnitude of 28 ft and a direction of 34 degrees west of north. Vector K has a magnitude of 48 ft and a direction of 20 degrees south of east. Find the magnitude and direction of their sum. a) 30 ft and 13 degrees north of east b) 36 ft and 54 degrees...

Vectors -- dot product and cross product? Hello may i know when to dot product and cross product?? both look to same to me..

Homework Statement question attached Homework Equations The Attempt at a Solution i can't understand III i can't understand what he wants , if he wants the ratio , the ratio between AP and PB was 3/5 which is not the same as OA and OB (λ=3/8)

What means: ? This guy, ##\vec{\nabla}_{\hat{\phi}} \hat{r}##, for example, means: \\ \hat{\phi}\cdot\vec{\nabla}\hat{r} = \begin{bmatrix} \phi _1 \\ \phi _2 \\ \end{bmatrix} \begin{bmatrix} \frac{\partial r_1}{\partial x} & \frac{\partial r_1}{\partial y} \\ \frac{\partial...

Homework Statement I have the equation: \mathbf{F}_{2,1} = \frac{Q_1 Q_2}{4 \pi \varepsilon_0 {r_{2,1}}^2}\hat{r}_{2,1} (standard electric force equation for 2 charges) I know the value of everything except Q2 and have to find it. The vectors each have 3 components. Normally in an...

Hi, I'm reading up on linear algebra and I'm wondering if the remark after a theorem I'm reading here is complete. The theorem states: "If {V_1,V_2,...,V_k} is an orthogonal set of nonzero vectors then these vectors are linearly independent." Remark after that simply states that if a set of...

I have an integral of aΘ cos(Θ) dΘ a is the unit vector for Θ. I'm not sure what to do with it in the integration. I know the unit vector equals a/abs(a) but that would give a mess of an integral cause of the abs(a).

From an exercise set on the summation convention: X and Y are given as [Xi] = \begin{pmatrix} 1\\ 0\\ 0\\ 1\end{pmatrix} and [Yi] = \begin{pmatrix} 0\\ 1\\ 1\\ 1\end{pmatrix} There are a few questions involving these vectors. The one I am stuck on asks to compute XiYj . It may be necessary...

Homework Statement Hi all , I have a problem statement , I know how to solve it but I don't know how to graph velocities so I can use cartesian coordinate and thus have correct answers. Would you please help me ?? A pitcher throws a fastball, which crosses the plate with a speed of 95 mph...

I am a little confused by an elementary point. Something must be wrong with the following: On one hand, a Hermitian operator (which is not necessarily unitary) takes one state to another state. Hence a state need not be represented as a unit vector; its norm can be greater (or less than)...

Mod note: Corrected a typo in the problem statement. [/color] Homework Statement IfIs the vector AP parallel to u? u= (1,4,-3) A(-2,-1,-2) The Attempt at a Solution I do know that if AP is parallel to u then there must be some scalar multiple such that Ax = u. I think it's a...

I am trying to derive the distribution for the sum of two random vectors, such that: \begin{align} X &= L_1 \cos \Theta_1 + L_2 \cos \Theta_2 \\ Y &= L_1 \sin \Theta_1 + L_2 \sin \Theta_2 \end{align} With: \begin{align} L_1 &\sim \mathcal{U}(0,m_1) \\ L_2 &\sim...

1) Let A a square matrix, x a colum vector and b another colum vector. So, I want solve for x the following equation: Ax=b So: x=b÷A = b×A-1 And this is the answer! Or would be this the correct answer x = A-1×b ? 2) Is possible to solve the equation above for A ? How?

Homework Statement From an alien spaceship Earth is in the direction (1, -8, -4) and Venus is in the direction (3, 12, 4). The average alien eye has a field of view of 5pi/6 radians. Without using arccos or calculating any exact angles, determine if the average one eyed alien on the spaceship...

Homework Statement Given following vectors in R4: v= (4,-9,-6,3) u = (5,-8,k,4) w=(s,-5,4,t) A. Find value of k if u and v are orthogonal B. Find values of S and T if w and u are orthogonal and w and v are orthogonal Homework Equations Orthogonal means dot product is zero...

Homework Statement An electron, with an initial horizontal velocity of magnitude 3.16 × 109 cm/s, travels into the region between two horizontal metal plates that are electrically charged. In that region, it travels a horizontal distance of 2.42 cm and has a constant downward acceleration of...

Homework Statement Let S be the subspace of all vectors in R4 that are orthogonal to each of the vectors (0, 4, 4, 2), (3, 4, -2, -4) What is an example of a matrix for which S is the nullspace? The Attempt at a Solution I'm not sure how I should be intepreting the question: [ 0 ,4 ,4 ,2...