1. Oct 14, 2012

troytroy

1. The problem statement, all variables and given/known data

consider the position vector expressed in terms of its cartesian components, r=xiei. Let w=wjej be a fixed vector whose components wj are constants that do not depend on the xi, so that δwj/δxi = 0

2. Relevant equations

I am trying to evaluate ∇((wXr)^2)

3. The attempt at a solution

2. Oct 14, 2012

gabbagabbahey

Hi troytroy, welcome to PF!

What have you tried and where are you stuck?

3. Oct 14, 2012

troytroy

I am getting confused on where to begin when using index notation for these kind of problems

4. Oct 14, 2012

gabbagabbahey

Well, here you are being asked to calulate the gradient of some scalar function, so a good place to start would be to look up the expression for the gradient of a general scalar function $f$ in index notation. What is that?

Next consider that in this case, the scalar function in question is the scalar product of of a vector with itself, $(\mathbf{w}\times\mathbf{r})^2$ (the norm-squared of a vector is usually written as $||\mathbf{v}||^2$, but some authors will use more clumsy notation and just call it $\mathbf{v}^2$. Either way the norm-squared of a vector is given by the scalar product of a vector with itself). So, how do you express the scalar product of a vector with itself in index notation?

Finally, consider that the vector whose norm-square you are taking the gradient of is, in this case, the cross product of a vector with another vector, $\mathbf{w}\times\mathbf{r}$. How do you represent a cross product like this in index notation?