Statement-1: If $\vec a,\vec b$ are non-zero and non-collinear vectors, then $\vec a×\vec b=[\vec a\,\, \vec b\,\,\hat i]\hat i +[\vec a\,\, \vec b\,\,\hat j]\hat j+[\vec a\,\, \vec b\,\,\hat k]\hat k$

Statement-2: For any vector $\vec r$

$\vec r=(\vec r.\hat i)\hat i+(\vec r.\hat j)\hat j+(\vec r.\hat k)\hat k$

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Clearly, statement-2 is true.

Replacing $\vec r$ by $\vec a ×\vec b$ in statement-2, we get statement-1. So statement-1 is true.

Hence, statement-2 is a correct explanation for statement-1.