The divergence of the vector field \[\overrightarrow {\rm{A}} = {\rm{x}}{{{\rm{\hat a}}}_{\rm{x}}} + {\rm{y}}{{{\rm{\hat a}}}_{\rm{y}}} + {\rm{z}}{{{\rm{\hat a}}}_{\rm{z}}}\] is A. 0 B. \[\frac{1}{3}\] C. 1 D. 3

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”[rac{1}{3}\
” option3=”1″ option4=”3″ correct=”option1″]

The divergence of a vector field is a measure of how much the vector field spreads out or converges at a point. It is defined as follows:

$$\nabla \cdot \overrightarrow{A} = \frac{\partial A_x}{\partial x} + \frac{\partial A_y}{\partial y} + \frac{\partial A_z}{\partial z}$$

In this case, the vector field is $\overrightarrow{A} = x\hat{\imath} + y\hat{\jmath} + z\hat{k}$. The divergence of this vector field is therefore:

$$\nabla \cdot \overrightarrow{A} = \frac{\partial x}{\partial x} + \frac{\partial y}{\partial y} + \frac{\partial z}{\partial z} = 1$$

Therefore, the correct answer is $\boxed{1}$.

The other options are incorrect because they do not represent the divergence of the vector field $\overrightarrow{A}$.

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