- #1
TheCanadian
- 367
- 13
I have a quantity defined as ## r =
\left|\vec{r} - \vec{r'}
\right|
## and am trying to take the gradient of this quantity. Now the gradient is with respect to the ordinary vector, ## \vec{r}##, and not ## \vec{r'} ##. But after looking at a solution, it says the direction of the gradient is in the direction parallel to ## \vec{r} - \vec{r'} ## and not ## \vec{r} ##. My apologies for being a bit vague here, but shouldn't the direction of the gradient be pointing in the direction in which the derivative is being taken (assuming only a radial component exists)? So if I am taking the derivative with respect to ## r ##, then it points in a direction parallel to ## \vec{r}##, while a derivative wrt to ##r - r' ## would point in ## \vec{r} - \vec{r'} ##?
\left|\vec{r} - \vec{r'}
\right|
## and am trying to take the gradient of this quantity. Now the gradient is with respect to the ordinary vector, ## \vec{r}##, and not ## \vec{r'} ##. But after looking at a solution, it says the direction of the gradient is in the direction parallel to ## \vec{r} - \vec{r'} ## and not ## \vec{r} ##. My apologies for being a bit vague here, but shouldn't the direction of the gradient be pointing in the direction in which the derivative is being taken (assuming only a radial component exists)? So if I am taking the derivative with respect to ## r ##, then it points in a direction parallel to ## \vec{r}##, while a derivative wrt to ##r - r' ## would point in ## \vec{r} - \vec{r'} ##?