Vectors Definition and 1000 Threads

I am in the process of reading through The Theoretical Minimum. One of the processes it suggests is relating to orthogonal vectors, particularly representing the right (|R>) and left (|L>) spins. Common sense says they're orthogonal but I was wondering how exactly to represent the inner product...

Homework Statement To simplify: ##\mid \vec b -\frac{\vec a*\vec b}{\vec a*\vec c} * \vec c \mid## ##\mid \vec b -\frac{(\vec a*\vec c)*(\vec b*\vec b)-(\vec a*\vec b)*(\vec b*\vec c)}{(\vec a*\vec b)*(\vec c*\vec c)-(\vec a*\vec c)*(\vec b*\vec c)} * \vec c \mid## Vectors may be any...

Homework Statement [/B]Homework Equations [/B]The Attempt at a Solution When I have to describe a motion I'm supposed to decompose a vector in two directions, for example in an inclined plane is decompose the weight in these directions: the normal to the plane and the parallel to the plane...

Homework Statement Prove the following: a) If ##P^a## is time-like and ##P^{a}S_{a}=0##, then ##S^{a}## is space-like. b) If ##P^a## is null and ##P^{a}S^{a}=0##, then ##S_{a}## is space-like or ##S^{a} \propto P^{a}##. Homework Equations Using the 'mostly minus' convention, ##A^a## is...

Hi pf, Having some trouble with basis vectors for expanding a given vector in 3-D space. Any given vector in 3-D space can be given by a sum of component vectors in the form: V = e1V1 + e2V2 + e3V3 (where e1, e2 and e3 are the same as i, j and k unit vectors). Equation 1. I am happy with...

Can someone please help me prove this product rule? I'm not accustomed to seeing the del operator used on a dot product. My understanding tells me that a dot product produces a scalar and I'm tempted to evaluate the left hand side as scalar 0 but the rule says it yields a vector. I'm very confused

Hi all. I have a question that is more about definitions or language, rather than physics. So (Euclidean) vectors used in Physics are "geometrical entities endowed with a magnitude and a direction". At least this is what i find if I look up "vector" in english speaking websites. My "problem"...

I know if the number of coordinates are same in both the old and new frame then A.B=A`.B` . But if the number of coordinates are not same in both old and new frame then A.B=0 means that both the vectors A and B are perpendicular. Why is it so that if the number of coordinates of both the frames...

Given a scalar function g defined on a manifold and a curve f:λ -> xa, the change of the function along the curve is \frac{dg}{d\lambda} = \frac{dg}{dx^{a}}\frac{dx^{a}}{d\lambda} = T^{a}\frac{dg}{dx^{a}} where \frac{dx^{a}}{d\lambda} = T^{a} is the tangent to the curve. The argument that I...

Hi there, I understand that taking the dot product of two four vectors automatically applies the metric tensor to the second vector. Is there a way to take write the dot product, using vector notation, in a way which keeps the signs of all of the components positive? Thanks in advance.

How many magnetic/electric flux vector one e- can produce? Only one or many? (Here I mean flux as force vectors and not a scalar quantity like in flux density.)

The wiki page https://en.wikipedia.org/wiki/Bell's theorem states the following which I agree with: Suppose the two particles are perfectly anti-correlated—in the sense that whenever both measured in the same direction, one gets identically opposite outcomes, when both measured in opposite...

Hey all, student100's brother here, he got me to create an account to ask my question here... I'm taking an introduction to linear algebra class and we had a test problem to prove a set of vectors is linear independent: ##V = v_1, \dots, v_n \in \Bbb R^n## such that each element of the set is...

Homework Statement Let s and t be scalars. show that u, v and su + tv are coplanar. u and v are arbitrary vectors, Homework EquationsThe Attempt at a Solution Well, i suppose if they are coplanar, triple scalar product of them should be 0, right? and su+tv is evidently a linear combination of...

Homework Statement Homework Equations Relevant equations can be derived from the formulas, by exchanging x to v, v to a, etc. The Attempt at a Solution I've tried to graph them, but I am not able to visualize or understand them. Please help me about these questions, I need some hints. If...

If you're driving in a car and map out all the displacement vectors, you can add the segments to get the total displacement. Correct? Why can't we add the various velocity vectors for the different segments to get the average velocity. ? Could you add up all the velocity vectors and divide by...

I am having a hard time understanding vector transformations. I know that vectors must transform a certain way and that dual vectors (or covectors) transform the "opposite" way. What is strange to me is that the basis vectors transform like dual vectors and the basis dual vectors transform like...

i am asked to determine whether 3 vectors which have 5 dimensions (x,y,z,w,u) are linearly dependent or independent in R^3. it doesn't make any sense. should i ignore w and u dimensions and take x,y,z only? because if i dont, all answers would be same, doesn't matter in r^3 or R^4 etc. the...

I have 2 vectors ##\vec {V}=(v_1,v_2,v_3,v_4...v_D)## and ##\vec {X}=(x_1,x_2,x_3,x_4...x_D)## in D-dimensional euclidean space. I want a tensor ,which is crosswise with both of them. I think that the tensor is parallel with (D-2)-dimensional area, am I right? I do not know a lot about tensors...

Homework Statement [/B] A block of mass 2kg is accelerated by the two forces F1 = 8i + 3j and F2 = -5i - 7j, (a) What is the net force on the block in unit vector notation, and what is its magnitude and direction? (b) What is the magnitude and direction of the acceleration?Homework Equations...

Homework Statement Solve for the forces P and N acting on an object in equilibrium on an inclined plane. Weight=10N, angle is 30 degrees http://blob:https%3A//www.physicsforums.com/d431a152-5681-411b-ba57-809320539165 Homework Equations Trigonometry, i.e. sin, cos, tan rules. The 'Z' rule...

In my text, it tells me to find the eigenvectors of a 2nd difference matrix and graph the eigenvectors to see how they fall onto sine curves. imgur link: http://i.imgur.com/oxbkTn6.jpg My question is simple but general. What does this even mean? How did they produce this graph from the...

Hello, My question is about using vector components to find a force in a particular direction. I already have the answer, I just don't understand it and would like an explanation if anyone has one. If I have two vectors with radial velocities (in this case it's measurements of ocean current...

NOTE: Thread was moved to Homework forums and thus has no homework template... I managed to find (a) but i couldn't figure out (b). I think OR = OP + PR = (2/3)a + t( (-1/15)a + (2/5)b) but i don't know how to go further please guide or help me with this please. Thanks

I'm tossing around an idea in my head, but I'm outside of my knowledge base. A guitar string is suspended between two points (nut and a bridge) and tightened to a certain tension. I assume most of the stress is in line with the strings, but force can do funny, counterintuitive things. I want...

In my textbook they used the right hand rule to show that rotation has vectors instead of just being positive or negative relative to its direction of rotation of a vinyl record. In the image the record was going clock wise so by the right hand rule it was going downward which makes sense, but...

I'm confused about what situations you should use unit vectors in... and it seems that when I approach the same problem using unit vectors vs. without unit vectors, I get different answers. Why? To illustrate my confusion, here's an example that I tried solving using unit vectors, and without...

hello. I'm looking for some general guidance as to which methods to use where. i'm wanting to find the force vectors on an object as it moves along a general curve in a space (imagine a roller coaster). for example the parametric curve. z=t x=cos(t) y=sin(t)I know i need to find the partial...

I'm attempting to learn the mathematics of quantum mechanics using textbooks such as "The Principles of Quantum Mechanics" by Dirac. I'm uncertain however of how ket vectors work! Say |A> + |B> = |C>, then what does |C> please represent?

I am trying to solve the following problem: Let A be a real mxn matrix. Describe the set of all vectors in F^m orthogonal to Col(A). Here, F^m could be C^m. Now in the real case, I'd say that the column space of A is the row space of A^T, and it is well known that the row space of a matrix is...

Homework Statement Let u = (2,k,1,-4) and v = (3,-1,6,-3) For which values of k is the distance d(u,v) = 6? Homework EquationsThe Attempt at a Solution 6 = √((3-2)2 + (-1-k)2 + (6-1)2 + (-3-4)2) 6 = √(1 + 1 + k2 + 25 + 21) 6 = √(k2 + 48) 36 = k2 + 48 k = √-12 The answers seem to be 6k, -16k...

Hi everyone. Aftrer doing a search I found loads of information but I still can't get my head around these damm vectors. I understand the basics and how to work out the dot product if given the question in a given way. An example of the questions I am being asked are: The following two...

Homework Statement Ok guys, I'm studying Physics and I started, of course, by learning about vectors. So I have this problem: There are two vectors: A (its length is 3 m) and B (its length is 4 m). I have not other informations about them. I want to know how I can dispose them to get a vector...

I have a Dicom Image that is interpreted as an array. Each cell is a pixel. Each pixel has a value. I want to find the vector components (x,y,z) of a pixel. Specifically, I want to find magnetic field vectors for each pixel. The image is for H1 atoms. Freq = 297, B0 = 3. How would you do this...

Homework Statement Illustrate the addition of the following two vectors and calculate the resulting vector: 55km [South] + 34km [North]. Homework EquationsThe Attempt at a Solution [/B] The attempt at the solution is below. What is troubling me is the overlap of the vectors and how to draw...

Homework Statement Determine the axial forces in the members of the truss and indicate whether they are in tension or compression. Homework Equations Fx = 0 Fy = 0 Mp = 0 The Attempt at a Solution I attempted to find the reactions at the supports first. So: Fx = 0 = Bx + 800cos(250)N Fy...

My linear algebra is a bit rusty. Let ##A=\{\bar{v}_1, \dots, \bar{v}_1\}## be a set of vectors in ##R^n##. Can dim(span##(A))=n## without spanning ##R^n##? I guess I'm unclear on how to interpret the dimension of the span of a set of vectors.

Homework Statement The 1.1m bar is supported by a ball and socket support at A and 2 smooth walls. The tension in the vertical cable CD is 1kN. Draw the Free Body Diagram of the Bar. Determine the Reactions at A and B. Homework Equations Equillibrium equations. Perhaps the vector...

[Moderator note: Post moved from New Member Introductions forum, so no template] I am having trouble understanding how to multiply unit vectors. I know that: (please excuse the notation) i^×j^ = k^ j^×k^ = i^ k^×i^ = j^ The question I am stuck on is: What is (i^×j^)×k^? So far I have (i^×j^)...

Homework Statement Hi! I just found this forum after trying to calculate something regarding a satellite's orbit. Hope that you can help me here. So, I need to calculate the matrix of a satellite's site vectors. I have found it in the ECEF form, but since the satellite is doing observations in...

Homework Statement A 1070-kg car is held in place by a light cable on a very smooth (frictionless) ramp, as shown in the figure(Figure 1) . The cable makes an angle of 31.0 ∘above the surface of the ramp, and the ramp itself rises at 25.0 ∘ above the horizontal. [/B] http://imgur.com/gkOQuRq...

Homework Statement (I roughly translate the problem statement from German) Given the vectors a = (1,-2,3) and b = (1,1,1), divide the vector a in two components a1 (parallel to b) and a2 (perpendicular to b). Homework Equations In a previous question of the problem, I found that: a.b = 2 a x...

Can you list as many axial vectors and polar vectors as possible?

Why work done by a force was taken as dot product between force applied and displacement caused?

hello i have browsed this forum for topics about this, and i found them very enlightening and helped a lot in terms of finding the length of the primitive vectors , the problem that i have is with the direction of said primitive vectors , while in fcc they are more or less easy to visualize in...

I'm trying to understand the maths of QM from Shankar's book - Principles of Quantum Mechanics: On page 21 of that book, there is a general derivation that if we have a relation: |v'> = Ω|v> Where Ω is a operator on |v> transfroming it into |v'>, then the matrix entries of the operator can be...

Hi, I'm doing a first course in GR and have just found out that \eta_{ab} = g(\vec{e}_{a}, \vec{e}_{b}) = \vec{e}_{a} \cdot \vec{e}_{b} where g is a tensor, here taking the basis vectors of the space as arguments. I haven't seen this written explicitly anywhere but does this mean that...

Hi. In GR , covariant differentiation is used because the basis vectors are not constant. But , what about in SR ? If the basis vectors are not Cartesian then they are not constant. Does covariant differentiation exist in SR ? And are for example spherical polar basis vectors which are not...

A very informal definition of a vector could be that it is a tuple of ordered numbers. As such we use the symbol ##\mathbb{R}^n## to refer to the set of vectors with real numbers and n many components. ##\mathbb{R}^2## refers to an element such as ##\vec{a} = (x, y)##. And ##\mathbb{R}^3##...

Homework Statement The moment of the couple is 600k (N-m). What is the angle A? F = 100N located at (5,0)m and pointed in the positive x and positive y direction -F = 100N located at (0,4)m and pointed in the negative x and negative y direction Homework Equations M = rxF M = DThe Attempt at a...