Is there a value of $\lambda$ for which $F$ is divergence free?

Question

For each $x=(x,y,z) \in \mathbb R^{3}$ define $|x|= \sqrt{x^{2}+y^{2}+z^{2}}$. Consider $F(x)=\frac{x}{|x|^{\lambda}}$, $x \neq 0$, $\lambda >0$.

1. Is there a value of $\lambda$ for which $F$ is divergence free?
2. Let $E: \mathbb R^3 \rightarrow \mathbb R^{3}$ be defined by $E(y)=q\frac{y}{|y|^3}$. Compute $\int_{S(x,a)} E\cdot n \, dA$, where $S$ is the sphere centered at $x$ and radius $a>0.$

My attempt: I think for divergence free, I need to compute the $\operatorname{div} F=0.$

I calculate the value of $\lambda=3$.

Is this answer is correct?

Anyone can give some idea of 2 part of this question?