$A$ unit vector perpendicular to vector $c$ and coplanar with vectors $a$ and $b$ is

Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three non-zero vectors such that $\vec{b} \cdot \vec{c} = 0$ and $\vec{a} \times (\vec{b} \times \vec{c}) = \frac{\vec{b} - \vec{c}}{2}$. If $\vec{d}$ is a vector such that $\vec{b} \cdot \vec{d} = \vec{a} \cdot \vec{b}$,then $(\vec{a} \times \vec{b}) \cdot (\vec{c} \times \vec{d})$ is equal to

Which of the following statements is true regarding the vector triple product $(a \times b) \times c$?

Which of the following is a true statement?

The vectors $\bar{a}$ and $\bar{b}$ are not perpendicular and $\overline{c}$ and $\overline{d}$ are two vectors satisfying $\overline{b} \times \overline{c} = \overline{b} \times \overline{d}$ and $\overline{a} \cdot \overline{d} = 0$. Then the vector $\overline{d}$ is equal to:

$(b \times c) \times (c \times a) = \dots$