Vectors Definition and 1000 Threads

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But the answer in my book is given that sec(theta) =3. Where am I going wrong?

I'm looking forward to have a better understanding of the polarization vector in quantum field theory in order to solve a particular problem. In class and in several textbooks I see that ##s^\mu=(0,\vec s)## and ##|\vec s|=1##. Are polarizations vectors defined to have no temporal component in...

I'm on to section 5.4 of Carroll's book on Schwarzschild geodesics and he says stuff in it which, I think, enlightens me on the use of Killing vectors. I had to go back to section 3.8 on Symmetries and Killing vectors. I now understand the following: A Killing vector satisfies $$...

A 45 kg chandelier is suspended by two chains of lengths 5 m and 8 m attached to two points in the ceiling 11 m apart. Find the tension in the 5 m rope.

Hi! I have a physics question I need help with. Bob can swim at 4 m/s in still water. He wishes to swim across a river 200 m wide to a point directly opposite from where he is standing. The river flows westward at 2.5 m/s and he is standing on the South bank of the river. a. What is the speed...

hi guys our solid state physics professor introduced to us this new concept of reciprocal lattice , and its vectors in k space ( i am still an undergrad) i find these concepts some how hard to visualize , i mean i don't really understand the k vector of the wave it elf and what it represents...

I know that any vector ##V## in Minkowski spacetime can be classified in three different categories based on its norm ##|V| = \sqrt{V \cdot V} = V^{\mu}V_{\mu}##. These are: 1) If ##V^{\mu}V_{\mu} < 0##, ##V^{\mu}## is timelike. 2) If ##V^{\mu}V_{\mu} > 0##, ##V^{\mu}## is spacelike. 3) If...

any tip to start?

The gradient transforms a scalar function into a vector function where the vector components are the rates of change of the functions with respect to its independent variables. Also, the properties of the gradient are: It lies in the plane. It is perpendicular to the level curves and points...

There are a few details, either convention or understanding, that I was hoping someone could help to clarify. Consider the object below, acted upon by a few forces including an unknown ##\vec{N}##, which I have split into its horizontal and vertical components ##\vec{N_{x}}## and...

I know this topic was raised many times at numerous forums and I read some of these discussions. However, I did not manage to find an answer for the following principal question. I gather one deals with the same set in both cases equipped it with two different structures (it is obvious if one...

Hey! :o We have that the vectrs $\vec{v},\vec{w}, \vec{u}$ are linearly independent. I want to check if the pairs $\vec{v}, \vec{v}+\vec{w}$ $\vec{v}+\vec{u}$, $\vec{w}+\vec{u}$ $\vec{v}+\vec{w}$, $\vec{v}-\vec{w}$ are linearly indeendent or not. Since $\vec{v}, \vec{w}, \vec{u}$...

Summary: Finding angle between vectors a and m, knowing magnitude of m and n, also the angle between m and n with 60 degrees. Using geometry, it looks like the angle is 30 degrees but the answer is suppose to be 54.7 degrees. I'm not sure how to solve this.

For a cylinder rolling down an inclined plane, does the tangential velocity of a point a distance R from the axis of rotation equal the velocity of the center of mass?

Hi everyone. I'm the only physics teacher at my school, so I have nobody to bounce ideas off of. I'm having a problem with students getting confused with direction when calculating net force. I teach an introductory physics course. It's the first time the students have ever seen physics and...

Hi all I am trying to get my head around resultant forces. I am happy that if I have a vector diagram with 2 forces I can work out graphically the resultant forces by connecting the head of one of the vectors to the tail of the second vector. The confusion comes in when I have 3 or more...

Homework Statement: Hallo. Can somebody explain to me what's the importance-use of unit vector in the below (second) equation? Why isn't the first equation just enough to describe r? What's the reason for unit vector to even exist? Homework Equations: in the photos

I have a little question about converting Velocity formula that is derived as, ##\vec{V}=\frac{d\vec{r}}{dt}=\frac{dx}{dt}\hat{x}+\frac{dy}{dt}\hat{y}+\frac{dz}{dt}\hat{z}## in Cartesian Coordinate Systems ##(x, y, z)##. I want to convert this into Polar Coordinate System ##(r, \theta)##...

I am admittedly entirely confused as to where to start, sorry. This is the diagram I'm given that fits with the rA + rB. If rB is 47.0 degrees above the x-axis normally, it would be the same counter-clockwise here, right? Then 180 - 47 = 133 degrees for the clockwise angle. But now I'm stuck...

I'm reading div grad curl for my math methods class, and I came across this question: "Using arrows of the proper magnitude and direction, sketch each of the following vector functions: (a) iy + jx, (b) (i + j)/√2 I don't understand the notation. Why is there an y and x next to the i and j in...

Homework Statement: The homework problem is included below, but I am looking at the derivatives of vectors. Homework Equations: I have the properties of derivatives below, but not sure they help me here...

Elementary question: Is there ever a case where the solutions for a wave equation turn out not to be a vector (in Hilbert space of infinite complex-valued dimensions, or a restriction to a subspace thereof) , but something else -- say, (higher-order) tensors or bivectors, or some such? My...

Hello, I was pondering on the following: a vector is a specific entity whose existence is independent of the coordinate system used to describe it. To start, I guess I need to state that we are describing the vector from the same reference frame using different coordinate systems (Cartesian...

Hey, this is a problem given to me by my prof for an assignment, and the TAs at my tutorials haven't been much help. Was wondering where to go with this question. Also, I'm a uni freshman who isn't used to the whole concept of proofs, and a lot of what my profs say seem to be a slew of...

Hello PF, here’s the setup: we have a geodesic congruence (not necessarily hypersurface orthogonal), and two sets of coordinates. One set, ##x^\alpha##, is just any arbitrary set of coordinates. The other set, ##(\tau,y^a)##, is defined such that ##\tau## labels each hypersurface (and...

v_1 = <-8/21,-20/21> v_2 = <50/21,-20/21> When I take the dot product of v_2 and <2,5> I get zero, indicating they are perpendicular. Sorry for the hand writing.

I'm stuck on a few Vector homework problems. I don't quite understand how to write vectors A+B and A-B for questions 1b and 2b. I tried starting with calculating the magnitude for vector A+B on question 1b and then followed by finding theta, but I'm not sure if that's what I'm supposed to do...

Trying to solve it

Well, I drew the polar and standard axis centered in the particle and wrote which angles were equal to 60° so I could decompose the velocity. The problem says "moves towards it (the radar) with velocity v=5 m/s, so that's one of the components. But I realized that the velocity "cuts" the angle...

You may be familiar with how you can express a vector field as a linear combination of basis vectors like so: X = Xi∂i Now, I know that normally, the basis vectors ∂i can be derived by taking the derivatives of the position vector for the coordinate system with respect to all the axes like...

1. I consider this problem algebraically, ##c\cdot \vec{u}+(1-c)\cdot \vec{v}=c(1,2)+(1-c)(2,1)=(c,2c)+(2-2c,1-c)=(2-c,1+c)##; since the constraint I know is ##c\geq 0##, I can conclude the expected vectors##(x,y)## must have ##x\leq2, y\geq 1##. 2. Similarly, I get...

I have some questions. Let us assume for these questions that I am using the (- + + +) sign convention. Firstly, we know that if you have a parameterized curve ξ(s), then you can find the proper time between two events at points s1 and s2 by using this formula (assuming that the curve is...

Classical problems for hookes law generally give either mass or spring constant. What if I have a graph of a wavelike structure that is oscillating which I can use to measure for example: T (period), t (time), Δx (displacement), v (velocity), a (acceleration) and other variables is this...

I don't know exactly where to start with this problem. But I'm going to try this, cos θ= adj/hyp cos 40° = Fx/100 Fx=100 cos 40° =76.60= 77N??

What is the advantage of using a polar coordinate system with rotating unit vectors? Kleppner's and Kolenkow's An Introduction to Mechanics states that base vectors ##\mathbf{ \hat{r}}## and ##\mathbf{\hat{\theta}}## have a variable direction, such that for a Cartesian coordinates system's base...

Suppose I have a system of two (possibly interacting) spins of 1/2. Then the state of each separate spin can be written as a ##\mathbb{C}^2## vector, and the spin operators are made from Pauli matrices, for instance the matrices ##\sigma_z \otimes \hat{1}## and ##\hat{1} \otimes \sigma_z##...

Greetings, I am having troubles with understanding the allowed k vectors in a crystal. Bloch's theorem gives us discrete energy bands for each wave vector k. However, only discrete k vectors are allowed. Using periodic boundary conditions, the discreteness is easy to show. But I am having a...

I have drawn a arrow pointing straight down (South) 110km and an arrow off that to the right(west) 70km.I know that the distance of the journey would be 180km. How do I go about finding the displacement?

Determine if the set of vectors $\begin{bmatrix} x\\y\\5 \end{bmatrix}\in \Bbb{R}^3$ form a vector space ok if I follow the book example I think this is what is done $\begin{bmatrix} x_1\\y_2\\5 \end{bmatrix} +\begin{bmatrix} x_2\\y_2\\5 \end{bmatrix} +\begin{bmatrix} x_2\\y_2\\5...

Ok, this is the notation I am going to use in this thread: uppercase means vectors, while "[V]c" means coordinates of vector V in frame c. I'm reading from a book: i have a reference frame "a" and a reference frame "b" rotated with respect to "a", the vector connecting the frames origin is R. We...

Source: https://mathinsight.org/vectors_cartesian_coordinates_2d_3d "A vector in three-dimensional space. A representation of a vector a=(a1,a2,a3)a=(a1,a2,a3) in the three-dimensional Cartesian coordinate system." My question is does representation of a vector to arbitrary precision require 3...

Can’t seems to find the degree

If i were to take one point as my origin and draw the two momentum, one for the initial collestion and one going from the wall after, from the origin point, then drawing horizontally i would get the answer as B as the resultant? Should i assume that for any resultant vector the direction can...

Let: ##\nabla## denote dell operator with respect to field coordinate (origin) ##\nabla'## denote dell operator with respect to source coordinates The electric field at origin due to an electric dipole distribution in volume ##V## having boundary ##S## is: \begin{align} \int_V...

Hi, I have a work-related problem to solve and I'm not sure where to start and a pointer would be appreciated. I have the following two sets of polar equations V1 + V2 = Vx V1 + V2 + V3 = Vy, where Vx, V3, and Vy have been measured with reasonable accuracy, maybe +/-2% Any thoughts on how to...

Hello, it is my first post here and I am not really sure whether this is the right section. I did not have the chance to take a look at the rules of the forum but I will as soon as I can (I feel a bit guilty for that, I'm sorry...). This is not "homework", I am just studying the amazing L&L...