Cross product Definition and 465 Threads

Homework Statement \bigtriangledown\times\\(v\times w)= v(\bigtriangledown\cdot w) - w(\bigtriangledown\cdot v)+ (v\cdot\bigtriangledown)w - (w\cdot\bigtriangledown) v I've tried expanding left side and get [v1(dw2/dy+dw3/dz)-w1(dv2/dy+dv3/dz)]i +...

Homework Statement If I have \vec{v}=\vec{\omega}\times\vec{r} how do I solve for omega? How do I "cross divide"? Scalar operations are easier, I know. But how do you do this vectorially?

Homework Statement Show that : || a x b||^2 = ||a||^2||b||^2 - (a . b)^2Homework Equations The Attempt at a Solution I don't know where to start off

http://img297.imageshack.us/img297/2527/physicsin9.jpg i've been working with the AxB in the first one, and found that |A||B|sin(theta) = A x B, and i thought i had found my theta to be 1 degree, but i don't believe that's right. also, when i attempted to do the dot product with the C vector...

[b]1. Show that the cross product is a continuous function. The Attempt at a Solution I have tried to apply the definition of continuity: find a delta such that |x-y|< delta implies |f(x)-f(y)|< epsilon but I'm having trouble making sense of what |x-y| is. As I see it, x is a pairs of...

Homework Statement A = -3i + 4j and B = 2i + 3j so I want to find AxB Homework Equations The Attempt at a Solution what I got is -9k + 8k, which is -k but the answer solution says it's -17k ?

Let U=a+jb, V=c+jd. What is U X V? Where "X" is the cross product. Can you explain?

Homework Statement Just wanted to ask what's the definition of the cross product between a vector and a range two tensor The Attempt at a Solution (x \times \hat{T})_{i\beta}=\epsilon_{ijk} x_j T_{k\beta}

Ug. My first try at this and my whole post was deleted. Here goes again :) Homework Statement i) Two cities on the surface of the Earth are represented by position vectors that connect the location of each city to the centre of the earth. Assuming that the centre of the Earth is assigned...

Hi folks, When you're squaring the sum of two vectors (v_1 + v_2)^2, why is it that it comes out as v_1 dot v_1 plus 2*v_1 dot v_2 plus v_2 dot v_2? Why do we use the dot product here instead of cross product? I understand that dot product is the multiplication of their parallel...

I've been using various methods of finding curvature, and using the forumla K=\frac{||\vec{r}'X \vec{r}''||}{||\vec{r}'||^3} I took the cross product of my two vectors and came up with (just assume this is correct, if my question isn't answered i'll post all related work)...

Homework Statement Vector A = 3.5i + 1.8j and vector B = 1.7i + 4.8j . Find the components of A x B: Homework Equations AxB = AB sin(theta) The Attempt at a Solution Since vector A=3.5i+1.8j and B=1.7i+4.8j, I translated that into vectors. So, A is 3.94 @ 27.77*, and B is 5.09 @...

http://en.wikipedia.org/wiki/Abuse_of_notation I don't want this thread to go too long. But can someone quickly explain to be how the Determinent method of evaluating the Cross Product is an "abuse". I cannot quite seem to grasp their explanation...

(This is part of a much larger problem) Homework Statement Find \hat{r} \times \hat{z} \times \hat{y} Homework Equations x=rsin(\theta)cos(\phi), y=rsin(\theta)sin(\phi),z=rcos(\theta) (cartesian->spherical) The Attempt at a Solution I decided...

I would like to know how to perform a cross product on polar coordinates. Thank You

Hi all, I have a general question. When calculating the area of a triangle in 3 space, one applies the formula 1/2||axb||. Given three vertices, a,b,c...does it matter which vectors we choose to use (ab, bc, ac) as our a b vectors? Thanks!

I guess one of them is scalor and one of them is vector, but what is the REAL DIFFERENCE between them? gracias

Statement to prove: If A and B are countable sets, prove A x B is countable. My work so far: I've thought of 2 ways to approach proving this. (1) I read that "Every subset of a countable set is again countable." So my first choice of proving this would be to state that it's given A and B...

I have a question about solving a problem involving a cross product. I understand how to find \vec{a} X \vec{b} = \vec{c}, but if \vec{a} and \vec{c} are given how do I find \vec{b}? Is there something I can do analogous to c/a =b? I've been reviewing my old calc III and linear algebra notes...

Homework Statement Show (A x B) dot (C x D) in terms of dot products only. Homework Equations A x B = ABsin(theta) A dot B = AB cos (theta) The Attempt at a Solution Subbing both those formulas into the top I got [ABsin(AtoB) times CDsin(CtoD) ] cos(between the two resultant...

Homework Statement Given vectors a=(1,-1,0,2,1) b=(3,1,-2,-1,0) and c=(1,5,2,4,-4), which are mutually orthogonal, find a system of linear equations that a vector x must satisfy so it is orthogonal to a, b, and c.Homework Equations None I think. The Attempt at a Solution This is part A of...

Homework Statement Point A is at (0,3,0), D(0, 0, 3), C(4, 0, 0) and B(x,y,z). The bar AB is 7.09 m long and is perpendicular to the bars AC and AD. Use the cross product to determine the coordinates of x, y, and z. Homework Equations The cross product matrix thing... The Attempt at a...

Hi everyone... I just wanted to know if you compute a cross product of two vectors in R^3, do you get a vector in R^3 or an actual value(say both vectors have actually values)... Another question. I did this in class but I wasn't sure how it would work. Let say I have a metrix 2x2. how do...

Homework Statement For the vectors in the figure below, with a = 8, b = 7, c = sqrt(113), give the magnitude and direction of the following cross products. (See attachment for figure/right triangle). (a) a x b (b) a x c (c) b x c Homework Equations \vec{A} \cdot...

The cross product equals to the area of the parallelogram defined by the two vectors (at least in R^3). So if working on vectors which units v_1 = (1,2,3)m v_2 = (3,4,5)m it correctly returns the according area. However, if used to get a vector perpendicular to each of the vectors the...

I have a 23 problem assignment due at the end of the week, and although I'm going to have a chance to talk to my teacher about the questions I have, I'd like to go ahead and get going on the problems. I've successfully completed 21 of them, but the last two are stumping me. I'm submitting them...

Prove the following? Vectors (v-w)x(v+w)=2(vxw)

I'm trying to track down the rationale for removing the cross product of velocity and magnetic field intensity from Maxwell's equation which specifies the value of the electric field intensity. In the third edition of "A Treatise on Electricity and Magnetism" Maxwell specifies (in modern...

I have not yet taken Linear Algebra, so perhaps that is why I don't have an answer to this question. But: Given a vector a <1,-1,0> and a vector b <-1,1,0>, I would suspect (by the right hand rule) that taking a X b, I would get a vector pointing out of the computer screen (assuming that...

This is a general question. If we have a parametric equation r(u,v) and we take r_u and r_v, then take their cross product, does it give us the gradient vector? Or just a vector parallel to the gradient vector?

Everything I have read indicates that the cross product is simply defined as a x b = i( ay*bz - az*by) - j( ax*bz - az*bx ) + k( ax*by - ay*bx ) and that it just so happens that there is a shorthand notation of cross product in matrix determinant form. How is the cross product...

"Stokes theorem" equivalent for cross product line integral Homework Statement I am aware that the vector path integral of a closed curve under certain conditions is equivalent to the flux of of the curl of the vector field through any surface bound by the closed path. In other words, Stokes...

Homework Statement Just a general questions I don't understand. Why is it sin A in a cross product and not cos A? I don't understand it in the equation F=qvBsinA Homework Equations no The Attempt at a Solution ...

Hey guys, I normally don't use forums for help but I've been stuck on these questions for some time now and I just want to see if there's anyone out there who can set me in the right direction. These questions are from a grade 12 Calculus and Vectors class and they relate to the cross product...

dot product and cross product. i (think dot product is like eg (1,2,4).(2,4,5) = 30 and cross product is like eg(1,2,4)x(2,4,5)=2, 8, 20) but I am not sure... and is there an order like in a.bxc do u do bxc and then.a or do u go normal left to right. but if left to right what's the rule in when...

I know how to compute it and how to use it in equations. I do not understand what is physically happening however. When you turn a disk to the right the angular momentum is the cross product of the forces so it goes perpendicular to them and away from you. To the left would be towards you...

What is the cross product of -i x i? Is it negative 1 or is still just 0?

[b]1. Find axb: Given the magnitude of lal=3 and the magnitude of lbl=2. [b]2. Since I have the magnitudes, I thought maybe I could use the equation of axb=lal lbl sin theta. [b]3. I thought since I am trying to find axb that I could use 90 as the angle theta to find axb. I am...

Homework Statement 1 (H_1 - H_2) \times \hat n = J_s 2 (H_1t - H_2t) = \hat n \times J_s How does one get from the first statement to the second statement? 3 H_{1t} - H_{2t} = J_s This is causing an interesting problem when I plug in numbers, I would have just left it with statement (3) but...

Force F = (9.0 N) i hat + (-4.0 N) k hat acts on a pebble with position vector r = (3.00 m) j hat + (-1.0 m) k hat, relative to the origin.(a) What is the resulting torque acting on the pebble about the origin? ( N·m) i hat + ( N·m) j hat + ( N·m) k hat (b) What is the resulting torque...

Hi. I have an integral of a cross product: \int a\times b(t)dt a does not depend on t. How can I move it outside? Is this legal: a\times\int b(t)dt ?

If vectors V_1 and V_2 are perpendicular, lV_1 x V_2l =? I know that if they are parallel for vector cross product, they equal 0.

Homework Statement Find the area of a triangle `PQR`, where `P=(0,4,4)`, `Q=(2,-6,-5)`, and `R=(-3,-5,6)` The Attempt at a Solution The vector PQ = (2, -10, -9) The vector PR = (-3, -9, 2) Using matrixes I set up something that looks like this... I J K 2 -10 -9 -3 -9...

Hello all, it might be funny! but i am stuck to it! what is the vector cross product formula in spherical and cylindrical coordinates?! I know for Cartesian coordinate we have that nice looking determinant. but what about the other coordinates. I had looks to all the math books (like...

Homework Statement Prove: (au) × v + (bu) × v = [(a + b)u] × v Homework Equations http://en.wikipedia.org/wiki/Cross_product The Attempt at a Solution u = ( x , y , z ) v = ( x₂, y₂,z₂) LHS: = (au) × v + (bu) × v = [ ay z₂- y₂az , - (axz₂- x₂az) , axy₂- x₂ay ] + [ by z₂- y₂bz , - (bxz₂-...

the question is: u = 9i-6j and v = 5i+bj for what value of b would u-v point in the same direction as w = 7i-3j? can anyone help me get started on this problem, I am not looking for answers just a little bit of help because I'm confused.. thanks

geometric algebra cross product -------------------------------------------------------------------------------- Homework Statement [/b] my text (Geometric Algebra for Physicists, by Doran and Lasenby), p. 69, deals with rotating frame {fsubk} (I assume in 3D) d/dt (fsubk) = omega X...

Homework Statement [/b] my text (Geometric Algebra for Physicists, by Doran and Lasenby), p. 69, deals with rotating frame {fsubk} (I assume in 3D) d/dt (fsubk) = omega X fsubk omega being angular velocity then omega X fsubk = (-I omega) dot fsubk = fsubk dot (I omega), where...

[SOLVED] Vector, cross product, and integral Homework Statement Evaluate: {\int \textbf{F} \times \texttt{d}\textbf{v}}. \textbf{F} and \textbf{v} are both vector fields in \mathbb{R}^3 Homework Equations \texttt{d}\textbf{v} = (\nabla \otimes \textbf{v} ) \texttt{d}\textbf{r} The Attempt...

If a, b, and c are vectors, and a=b x c, and a and c are known, how do I solve for b? b=a/c ? I don't think we've covered diving vectors, and since the cross-product is a special case of multiplying vectors (as opposed to dot product), I'm not sure this is allowed anyway. I'm trying to...