Starting with LHS:
êi εijk Aj (∇xA)k
êi εijk εlmk Aj (d/dxl) Am
(δil δjm - δim δjl) Aj (d/dxl) Am êi
δil δjm Aj (d/dxl) Am êi - δim δjl Aj (d/dxl) Am êi
Aj (d/dxi) Aj êi - Aj (d/dxj) Ai êi
At this point, the LHS should equal the RHS in the problem statement, but I have no clue where...
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...
Hi
I have used cross products thousands of time without really knowing what it actually does; I know how to compute it, but I don't feel like I understand it. Also, when it shows up in physics/kinematics contexts, it's only because the magnitudes of the vectors involved have to be multiplied...
1. Homework Statement
Calculate |u+v+w|, knowing that u, v, and w are vectors in space such that
|u|=√2, |v|=√3, u is perpendicular to v, w=u×v.
2. Homework Equations
|w|=|u×v|=|u|*|v|*sinΘ
3. The Attempt at a Solution
Θ=90°
|w|=(√2)*(√3)*sin(90°)=√(6)
Then I tried to use
u={√2,0,0}...
We all know that the area of a triangle having consecutive sides as ##\vec { a }## and ##\vec { b }## has the area ##\frac { 1 } { 2 } | \vec { a } \times \vec { b } |## but what is the direction of that area vector? I mean if we consider ##\vec { a } \times \vec { b }## that will be one...
1. Homework Statement
A 2.4 kg particle-like object moves in a plane with velocity components vx = 25 m/s and vy = 80 m/s as it passes through the point with (x, y)coordinates of (3.0, −4.0) m. (Express your answers in vector form.)
(a) What is its angular momentum relative to the origin at...
This is more of a general question, but I've encountered this kind of exercises a lot in my current preperations for my exam:
There are two cases but the excercise is pretty much the same:
Compute
$$(1) \space \operatorname{div}\vec{A}(\vec{r}) \qquad , where \thinspace...
(First, I am aware there is no cross product in higher dimensions. I am aware of differential forms. I am aware of the problems with the cross product. I know enough to know what I don't know. but set all that aside.)
With that, could someone help me, by properly phrasing the cross product...
1. Homework Statement
Given that vector a = (1, 2, -5), b = (-12, 41, 75) and c = a + 2b, explain why (without doing any calculations whatsoever) the value of a•(b x c) = 0
2. Homework Equations
No specific equations, as the question asks for the value without making any calculations. This...
Hello people,
I'm a little bit confused about how to define the polarization direction for TM/TE mode.
Take a look at the TE mode picture I found in some place.
Picture1
The Cartesian system of coordinate (XYZ) here is chosen by the right hand rule.
Picture2
But how we chose the direction...
Could someone tell me if this 4-Vector cross product is correct:
i j k t
dx dy dz 1/c*dt
Ex Ey Ez Et
=[(dy(Ez)-dz(Ey))-(dy(Et)-1/c*dt(Ey))+(dz(Et)-1/c*dt(Ez))]*i
-[(d(E)-d(E))-(d(E)-d(E))+(d(E)-d(E))]*j...
Hello
I need help to explain the affect of the cross product without the its current symbolism, but for angular momentum.
I can explain angular momentum in terms of the cross product of 3D space formulated like this:
|r| |v| * sin(angler.v) e-perp to r and v Eq.1
(I can explain this to...
Okay so, I am wondering if it is possible to find the actual cross product (not the magnitude of the cross product) from this information
1. magnitude of both vectors
2.angle between vectors
3.plane the vectors lie in
Is there any way to calculate that cross product vector?
Thank you very much...
Can anybody give me a list of all cross products in physics. I have the following in my list:
Torque
$$\vec{\tau}=\vec{F}\times\vec{r}$$
Angular momentum
$$\vec{L}=\vec{r}\times\vec{p}$$
Velocity
$$\vec{v}=\vec{\omega}\times\vec{r}$$
Biot-Savart law
$$\vec{dB}=\dfrac{\vec{i...
I understand that the torque on a gyrating object is defined as the force vector cross multiplied by the lever arm position vector, which produces a resultant vector that is normal to both of the original vectors. However, when an object (let's say a disk) is rotating about an axis...
1. Homework Statement
Given the figure below
I need to calculate the total magnetic force on the semicircle section of the conductor.
Current is I, Radius is R, and the Magnetic Field is B.
2. Homework Equations
d\vec{F} = Id\vec{l} \times \vec{B}
3. The Attempt at a Solution
dl is equal...
1. Homework Statement
Suppose r:R\rightarrow { V }_{ 3 } is a twice-differentiable curve with central acceleration, that is, \ddot { r } is parallel with r.
a. Prove N=r\times \dot { r } is constant
b. Assuming N\neq 0, prove that r lies in the plane through the origin with normal N.
2...
1. Homework Statement
The three vectors A, B, and C point from the origin O to the three corners of a triangle. Show that the area of the triangle is given by 1/2|(BxC)+(CxA)+(AxB)|.
2. Homework Equations
3. The Attempt at a Solution
I know that the magnitude of the cross product of any...
1. Homework Statement
A\cdot B\times C\quad =\quad 2\\ (2A+B)\quad \cdot \quad [(A-C)\quad \times \quad (2B+C)]\quad =\quad ?
2. Homework Equations
Various cross product and dot product properties
3. The Attempt at a Solution
I've only managed to get so far, don't really know what to do...
I am trying to derive the law of signs from the cross product.
First, we have three vectors ##\vec{A} ~\vec{B} ~\vec{C}## such that ##\vec{A} + \vec{B} + \vec{C} = 0##. This creates a triangle. Then, we label the angles opposite the respective sides as a, b, and c. I am not sure where to go...
If we seek a bijection $$\wedge^p V \to \wedge^{n-p} V$$ for some inner product space ##V##, we might think of starting with the unit ##n##-vector and removing dimensions associated with the original vector in ##\wedge^p V ##. Might this be expressed as a sequence of steps by some binary...
1. Homework Statement
I was checking my work and Chegg uses the equations differently. Can somebody tell me why? Maybe I'm misunderstanding how/why to use the equation I chose.
2. Homework Equations
They say aB = -ω2ABRB/Ai
I used aB = aA + αk x r - ω2rB/A
3. The Attempt at a Solution...
1. Homework Statement
Hi everyone,
I am a first year physics student and we recently learned about torque.
Every time I think I understand it something else comes up to confuse me - this time it is the direction. I tried looking in the forum and generally in google, but everyone only explains...
1. Homework Statement
A rotational axis is directed perpendicular to the plane of a square and is located as shown in the drawing. Two forces, F1 and F2, are applied to diagonally opposite corners, and act along the sides of the square, first as shown in part a and then as shown in part b of...
So its been a while since I studied maxwells equations, anyway:
So From my ignorant perspective, trying to derive conceptual meaning from these, I can see that the time dependant study there is some conductivity x the partial differential of the magnetic vector potential plus the cross product...
Hi,
I was just wondering if you have a cross product can you multiply out the constants and put them to one side.
So ik x ik x E is equal to i^2(k x k x E) therefore is equal to -k x k x E.
Is that correct?
1. Homework Statement
The diagram shows a box with parallel faces. Two of the faces are trapezoids and four of the faces are rectangles. The vectors A, B, and C lie along the edges as shown, and their magnitudes are the lengths of the edges. Define the necessary additional symbols and prove...
1. The problem is:
( a x b )⋅[( b x c ) x ( c x a )] = [a,b,c]^2 = [ a⋅( b x c )]^2
I am supposed to solve this using index notation.... and I am having some problems.
2. Homework Equations : I guess I just don't understand the finer points of index notation. Every time I think I am getting...