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

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

Let $\vec{a}=-\hat{i}+\hat{j}+2\hat{k}$, $\vec{b}=\hat{i}-\hat{j}-3\hat{k}$, $\vec{c}=\vec{a}\times\vec{b}$ and $\vec{d}=\vec{c}\times\vec{a}$. Then $(\vec{a}-\vec{b}) \cdot \vec{d}$ is equal to :

Let $\vec{a} = \hat{i} + \hat{j}$, $\vec{c} = \hat{i} - \hat{j}$ and a vector $\vec{b}$ be such that $\vec{a} \times \vec{b} = \vec{c}$ and $\vec{a} \cdot \vec{b} = 3$. Then $|\vec{b}| = $

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

$\overrightarrow{a} \times [\overrightarrow{a} \times (\overrightarrow{a} \times \overrightarrow{b})]$ is equal to