Simplify $grad(\vec{a} \cdot \vec{x})$, where $\vec{a}$ is a constant vector.
My attempt: \begin{align} grad(\vec{a} \cdot \vec{x})&=grad(a_1x+a_2y+a_3z)\\ & = \frac{\partial (a_1x+a_2y+a_3z)}{\partial x}+\frac{\partial (a_1x+a_2y+a_3z)}{\partial y}+ \frac{\partial (a_1x+a_2y+a_3z)}{\partial z}\\ & = a_1+a_2+a_3 \end{align}
But this does not equal the answer $\vec{a}$.
You are missing the directions in each term
$$ \nabla f = \frac{\partial f}{\partial x}\color{blue}{\hat{x}} + \frac{\partial f}{\partial y}\color{blue}{\hat{y}} + \frac{\partial f}{\partial z}\color{blue}{\hat{z}} $$
So in your case
\begin{eqnarray} \nabla ({\bf a}\cdot {\bf x}) &=& \frac{\partial ({\bf a}\cdot {\bf x}) }{\partial x}\color{blue}{\hat{x}} + \frac{\partial ({\bf a}\cdot {\bf x}) }{\partial y}\color{blue}{\hat{y}} + \frac{\partial ({\bf a}\cdot {\bf x}) }{\partial z}\color{blue}{\hat{z}} \\ &=& a_1 \color{blue}{\hat{x}} + a_2 \color{blue}{\hat{y}} + a_3 \color{blue}{\hat{z}} = {\bf a} \end{eqnarray}