Using 3D cylindrical coordinates, I get 0 as the answer.

$$ \nabla^{2} (k \hat{r}) = \hat{r} (\frac{1}{r} \frac{\partial }{\partial r}\left(r \frac{\partial (k)}{\partial r}\right) + 0 + 0) + \hat{\phi} [\nabla^{2}(0)] + \hat{z} [\nabla^{2}(0)]= 0$$

Am I correct?

The solution to this question in the book that I'm using has ignored the unit vector and has given the Laplacian of $kr$ instead which is $k/r$.

Using 3D cylindrical coordinates, I get 0 as the answer.

$$ \nabla^{2} (k \hat{r}) = \hat{r} (\frac{1}{r} \frac{\partial }{\partial r}\left(r \frac{\partial (k)}{\partial r}\right) + 0 + 0) + \hat{\phi} [\nabla^{2}(0)] + \hat{z} [\nabla^{2}(0)]= 0$$

Am I correct? (Edit: I'm not)

The solution to this question in the book that I'm using has ignored the unit vector and has given the Laplacian of $kr$ instead which is $k/r$.

Edit: Directly applying $\nabla^2\mathbf A=\nabla(\nabla\cdot\mathbf A)-\nabla\times\nabla\times\mathbf A$ gave me the answer $\frac{-k}{r^2} \hat{r}$ which is correct according to the expression for vector Laplacian in cylindrical coordinates given on page 60 of this pdf: https://ws.engr.illinois.edu/sitemanager/getfile.asp?id=135 Thanks everyone for the replies.

Using cylindrical coordinates, I get 0 as the answer.

$$ \nabla^{2} (k \hat{r}) = \hat{r} (\frac{1}{r} \frac{\partial }{\partial r}\left(r \frac{\partial (k)}{\partial r}\right) + 0 + 0) + \hat{\phi} [\nabla^{2}(0)] + \hat{z} [\nabla^{2}(0)]= 0$$

Am I correct?

The solution to this question in the book that I'm using has ignored the unit vector and has given the Laplacian of $kr$ instead which is $k/r$.

Using 3D cylindrical coordinates, I get 0 as the answer.

$$ \nabla^{2} (k \hat{r}) = \hat{r} (\frac{1}{r} \frac{\partial }{\partial r}\left(r \frac{\partial (k)}{\partial r}\right) + 0 + 0) + \hat{\phi} [\nabla^{2}(0)] + \hat{z} [\nabla^{2}(0)]= 0$$

Am I correct?

The solution to this question in the book that I'm using has ignored the unit vector and has given the Laplacian of $kr$ instead which is $k/r$.

Using cylindrical coordinates, I get 0 as the answer.

$$ \nabla^{2} (k \hat{r}) = \hat{r} (\frac{1}{r} \frac{\partial }{\partial r}\left(r \frac{\partial (k)}{\partial r}\right) + 0 + 0) + \hat{\phi} [\nabla^{2}(0)] + \hat{z} [\nabla^{2}(0)]= 0$$

Am I correct?

The solution to this question in the book that I'm using has ignored the unit vector and has given the Laplacian of kr instead which is k/r.

Using cylindrical coordinates, I get 0 as the answer.

$$ \nabla^{2} (k \hat{r}) = \hat{r} (\frac{1}{r} \frac{\partial }{\partial r}\left(r \frac{\partial (k)}{\partial r}\right) + 0 + 0) + \hat{\phi} [\nabla^{2}(0)] + \hat{z} [\nabla^{2}(0)]= 0$$

Am I correct?

The solution to this question in the book that I'm using has ignored the unit vector and has given the Laplacian of $kr$ instead which is $k/r$.