If for any three non-null vectors ​​$$\vec{a}, \vec{b}, \vec{c}, \quad (\vec{a} \times \vec{b}) \times \vec{c} = \vec{a} \times (\vec{b} \times \vec{c})$$ then​

Correct option is D

​$$\textbf{Solution:}\\ (\vec{a} \times \vec{b}) \times \vec{c} = \vec{a} \times (\vec{b} \times \vec{c}) \\[8pt]\text{Use test vectors: } \vec{a} = \hat{i}, \vec{b} = \hat{j}, \vec{c} = \hat{k} \\[4pt]\vec{a} \times \vec{b} = \hat{k}, \quad (\vec{a} \times \vec{b}) \times \vec{c} = \hat{k} \times \hat{k} = \vec{0} \\\vec{b} \times \vec{c} = \hat{i}, \quad \vec{a} \times (\vec{b} \times \vec{c}) = \hat{i} \times \hat{i} = \vec{0} \\[6pt]\text{Thus, } \vec{b} = \hat{j}, \quad \vec{a} \times \vec{c} = \hat{i} \times \hat{k} = -\hat{j} \\[4pt]\Rightarrow \vec{b} \text{ and } \vec{a} \times \vec{c} \text{ are parallel} \\[12pt]\boxed{\text{Correct answer: (D)}}$$​​