# Math Help - Proving vector calculus relationships

1. ## Proving vector calculus relationships

How would you go about proving:

Curl(f(r)R) where R is the position vector x^(2)i +y^(2)j +z^(2)k

I know it should equal zero but once Ihave it in its components I am struggling to make them equal zero.

Thank you

2. ## Re: Proving vector calculus relationships

so basically the curl is evaluates to $\begin{bmatrix}\frac{\partial}{\partial{y}}z^2 - \frac{\partial}{\partial{z}}y^2 \\ \frac{\partial}{\partial{x}}z^2 - \frac{\partial}{\partial{z}}x^2 \\ \frac{\partial}{\partial{x}}y^2 - \frac{\partial}{\partial{y}}x^2 \end{bmatrix}$ which is clearly $\begin{bmatrix} 0\\0\\0 \end{bmatrix}$

3. ## Re: Proving vector calculus relationships

Trianagt, to use jakncokes' answer you will also need to know that $\nabla\times (f\vec{v})= \nabla f\times v+ f\nabla\times v$