I'm just getting comfortable with the use of index (Einstein) notation, but having not dealt with vectors for a couple of years I'm a little stuck.
For the following problem:
$$\bar \Delta (\bar c \cdot \bar r)$$
Where $\bar c$ is a constant vector and $\bar r$ is a position vector.
The solution to the problem is :
$$\bar c$$
I thought that the first line of working might be:
$$\partial_i (c_j r_j)_i$$
But I'm not sure if this is to correct…or what to do next.
Thanks in advance for your help!
Best Answer
I know the answer so I thought I'd put it in for any Googlers.
$$ \bar \Delta (\bar c \cdot \bar r)$$
LHS:
$$ d_i (c_j r_j) $$
$$ = c_j \delta_{ij} $$
$$ = c_i $$
$$ = \bar c$$