In the cube of side 'a' shown in the figure, the vector from the central point of the face ABOD to the central point of the face BEFO will be:

A

$$\frac{1}{2}a(\hat{k} - \hat{i})$$

B

$$\frac{1}{2}a(\hat{i} - \hat{k})$$

C

$$\frac{1}{2}a(\hat{j} - \hat{i})$$

D

$$\frac{1}{2}a(\hat{j} - \hat{k})$$