1
vote
2answers
38 views

is it necessary that curl of 2d vector is perpendicular to the plane.

I am just confused, help me guys. The question comes up, because we say that curl is either clockwise or anti-clockwise at a point.
5
votes
4answers
58 views

Proof: Force always perpendicular and motion in a plane implies that the trajectory is a circle

I am looking for a proof for a physics problem. Consider a particle which is subject to a force $\vec{F}(t)$ with $|\vec{F}(t)| = \text{const}$ which is always perpendicular to the velocity ...
0
votes
2answers
25 views

Helmholtz decomposition - motivation

Our lecturer presented us the Helmholtz decomposition of smooth vector fields. He added a proof, but he didn't provide any single motivation - e.g. where Helmholtz used the decomposition or for which ...
0
votes
1answer
45 views

How to prove sum of vectors with same magnitude is equal to zero.

Suppose that we have $n$ vectors $v_1,v_2...v_n$ with same magnitude in plane s.t. the angle between $v_i$ and $v_{i+1}$ is $2\pi/n$ then $v_1+v_2+...v_n=0$ for all $n \geq 2$. I can show this by ...
1
vote
2answers
31 views

Finding the magnitude of a vector product between two vectors?

Vector $\overrightarrow{A}$ has magnitude $11.0m$ and vector $\overrightarrow{B}$ has magnitude $16.0m$ . The scalar product $\overrightarrow{A}\bullet \overrightarrow{B}$ is $79.0m^2$. What is the ...
0
votes
1answer
98 views

Physics Vector Problem - Airplane

Heres the question: A plane leaves the airport in Galisto and flies $140$km at $68.0^∘$ east of north and then changes direction to fly $255$km at $48.0^∘$ south of east, after which it makes an ...
0
votes
1answer
47 views

How to determine the magnitude of a resultant vector?

I was able to determine a resultant vector based on the sum of two vectors and told to express them in vector units. Here is my answer that was correct: ...
0
votes
2answers
120 views

Tensor Projection

I'm currently reading "Vector and Tensor Analysis with Applications" by A.I. Borisenko and I.E. Tarapov, and I'm having trouble following a particular mathematical step in where the author projects ...
0
votes
0answers
71 views

vector function for finding position vectors on same ray in two concentric spheres

I need a vector function for finding two position vectors which are each on the same ray, and which each orbit on concentric spheres around a given center $\{cx,cy, cz\}$ The first position vector ...
6
votes
3answers
105 views

A Weird Contradiction about angular momentum operator in quantum mechanics

I am starting with the standard definition of an angular momentum operator in quantum mechanics given as $$\mathbf{L} = k(\mathbf{r}\times\mathbf{p}) = k(\mathbf{r}\times\nabla),$$ where ...
2
votes
1answer
144 views

Trouble understanding a common vector calculus example

I have difficulty understanding the following vector calculus example. Text can be found here. It is the 5th Q&A -- starting with equation (31.1035).It concerns finding the vector potential of a ...
1
vote
1answer
143 views

Let $F(x,y,z) = -c(r/||r||^3)$ be the force resulting from the inverse square law…

$c$ is a constant and $r = (x,y,z)$. Show that $\displaystyle f(x,y,z) = \frac{c}{\sqrt{x^2+y^2+z^2}}$ is a potential function for $F$. What can be concluded from any path from point $A$ to point $B$ ...
1
vote
1answer
355 views

Parametric curve of intersection - line integral with respect to arc length

This comes from Apostol's Calculus, Vol. II, Section 10.9 #14: A uniform wire has the shape of that portion of the curve of intersecion of the two surfaces $x^2+y^2=z^2$ and $y^2=x$ connecting the ...
0
votes
2answers
107 views

Determine the flow and amplitude equation for thermal energy (with Del operator)

It is a question vector calculus and Maxwell's laws. I put it this way. Let's say, we are working in a $3$-Dimensional space ( e.g $x\cdot y\cdot z = 4\cdot3\cdot2$, a certain room/class of that size ...
2
votes
1answer
107 views

How to prove the existence of the following equation?

I learned electrodynamics. According to the vector potential determination, $$ \mathbf B = [\nabla \times \mathbf A ], $$ Coulomb gauge, $$ \nabla \mathbf A = 0, $$ and one of Maxwell's equations, $$ ...
1
vote
2answers
2k views

Finding the component of a vector tangent to a circle

Problem Given a vector and a circle in a plane, I'm trying to find the component of the vector that is tangent to the circle. The location of the tangent vector is unimportant; I only need to know ...
1
vote
1answer
122 views

Help with volume integration

I need help solving this integral ($\hat{z}$ denotes the polar axis):$$\int_V\dfrac{\vec{r}\cdot(\vec{r}-c\hat{z})}{|\vec{r}|^3|\vec{r}-c\hat{z}|^3} dV$$ Where $V$ denotes all space. Attempt: $$2\pi ...
1
vote
1answer
461 views

What is this question asking about vector components?

Here's a question from my homework: Two vectors are given by a = 1.9i + 3.2j and b = 1.6i + 8.6j. Find (a)|a × b|, (b)a · b, (c)(a + b) · b, and (d) the component of a along the direction of ...
2
votes
1answer
353 views

Illustration of vector calculus vs. differential forms

I am looking for a nice illustration of how vector calculus relates to differential forms. A demonstration that employs physics is appreciable (e.g. electromagnetism). In particular, while dualizing ...
0
votes
1answer
6k views

how to calculate the angle in the x-y, y-z, x-z plane given only 3D vector direction and magnitude?

Please help me solve this. I have been thinking of all sorts of ways to solve this but can't figure out how :(. Ok here's the problem: I am given a three dimensional velocity vector (i know the ...