Obtain scalar product in terms of Cartesian component of vectors.

If $\overrightarrow A  \times \overrightarrow B = \overrightarrow C + \overrightarrow D,$ then select the correct alternative-

For any two vectors $\overrightarrow A $ and $\overrightarrow B $, if $\overrightarrow A \,.\,\overrightarrow B = \,\,|\overrightarrow A \times \overrightarrow B |,$ the magnitude of $\overrightarrow C = \overrightarrow A + \overrightarrow B $ is equal to

If for two vectors $\overrightarrow A $ and $\overrightarrow B ,\overrightarrow A \times \overrightarrow B = 0,$ the vectors