Question

Verify the identity in which \(\vec{a}\) is a constant vector, \(\vec{r}=x\hat{i}+y\hat{j}+z\hat{k}\), and \(r=||\vec{r}||\) \[\nabla r=\frac{\vec{r}}{r}\]

Answer 1

oops, damn brackets. (the bottom is what I need to verify)\[r=||\vec{r}||\]\[\nabla r=\frac{\vec{r}}{r}\]

Answer 2

find each...
what is \[\|\vec r\|\] ?

Answer 3

sorry I typed it wrong.

Verify the identity in which a⃗ is a constant vector, \(\vec{r}=x\hat{i}+y\hat{j}+z\hat{k}\) and \(r=||\vec{r}||\) \[\nabla r=\frac{\vec{r}}{r}\]

and ||r|| is simply the length of r

Answer 4

I'm not sure I understand the question

Answer 5

Basically I need to verify that \[\nabla r=\frac{\vec{r}}{||r||}\]

Answer 6

I believe some vector Geometry might help us here.

Answer 7

So if we divide the vector (and therefore also it's components) we obtain a unit vector of length one, just in an altered direction.