For any three vectors $a, b, c$,the condition $a \times (b \times c) = (a \times b) \times c$ holds if:

If $\overline{a}=\frac{1}{\sqrt{10}}(4 \hat{i}-3 \hat{j}+\hat{k})$ and $\overline{b}=\frac{1}{3}(\hat{i}+2 \hat{j}+2 \hat{k})$,then the value of $(2 \bar{a}-\bar{b}) \cdot \{(\bar{a} \times \bar{b}) \times (\bar{a}+2 \bar{b})\}$ is

If $\bar{x} \cdot \bar{y} = 0$,then $\bar{x} \times (\bar{x} \times \bar{y}) = \dots$ where $|\bar{x}| = 1$.

If $\bar{a}=\frac{1}{\sqrt{10}}(3 \hat{\imath}+\hat{k})$ and $\bar{b}=\frac{1}{7}(2 \hat{\imath}+3 \hat{\jmath}-6 \hat{k})$,then the value of $(2 \bar{a}-\bar{b}) \cdot[(\bar{a} \times \bar{b}) \times(\bar{a}+2 \bar{b})]$ is

If $a, b, c, d$ are coplanar vectors,then $(a \times b) \times (c \times d) = $

If $a = i + j - k$,$b = i - j + k$,and $c = i - j - k$,then $a \times (b \times c) = \dots$