Let $a, b, c$ be three vectors. Then $a \times (b \times c) = (a \times b) \times c$ if:

If $\overline{b}$ and $\overline{c}$ are unit vectors and $|\bar{a}|=7$,$\bar{a} \times(\bar{b} \times \bar{c})+\bar{b} \times(\bar{c} \times \bar{a})=\frac{1}{2} \bar{a}$,then the angle between the vectors $\bar{a}$ and $\overline{c}$ and the angle between the vectors $\overline{b}$ and $\overline{c}$ are respectively.

Let $\bar{a}, \bar{b}$ and $\bar{c}$ be three vectors having magnitudes $1, 1$ and $2$ respectively. If $\bar{a} \times(\bar{a} \times \bar{c})+\bar{b}=\bar{0}$,then the acute angle between $\bar{a}$ and $\bar{c}$ is

If $\vec{a}, \vec{b}, \vec{c}$ are three non-zero and non-coplanar vectors such that $\vec{a} \times (\vec{b} \times \vec{c}) = \frac{\vec{b}}{2}$, then the angle between $\vec{a}$ and $\vec{b}$ is ...

If $a = 3i - j + 2k,$ $b = 2i + j - k$ and $c = i - 2j + 2k,$ then $(a \times b) \times c$ is equal to

If $\bar{a}, \bar{b}, \bar{c}$ are non-coplanar unit vectors such that $\bar{a} \times (\bar{b} \times \bar{c}) = \frac{\bar{b} + \bar{c}}{\sqrt{2}}$,then the angle between $\bar{a}$ and $\bar{b}$ is: