I am quite new to vector calculus and I am not sure how to calculate the following.
Suppose we have three position vectors $\vec{r}_i$,$\vec{r}_j$, and $\vec{r}_k$ in $R^3$.
The angle $\theta_{ijk}$ is the angle between the vector $\vec{r}_{ij}=\vec{r}_i-\vec{r}_j$ and the vector $\vec{r}_{ik}=\vec{r}_i-\vec{r}_k$.
I am interested in calculating the following gradient of the cosine angle: $\nabla_{\vec{r}_j} \cos(\theta_{ijk})$.
Edit 1 : As pointed out by Travis, the notation above may not make sense. What about the following notation? $\partial\cos(\theta_{ijk})/\partial \vec{r}_j$. I apologize for any nonsense.
How would I compute this? Coud you also tell me a good introductory book?
Thanks.