Question

a'. Vector (b' vector ×c' vector)=1/(a vector ×b vector)c vector

Answer 1

Triple product

$$\vec a\cdot(\vec b\times\vec c)=(\vec a\times\vec b)\cdot\vec c$$

Given

$$\vec a\cdot(\vec b\times\vec c)=\dfrac{1}{(\vec a\times\vec b)\cdot\vec c}$$

Then

$$\bigg(\vec a\cdot(\vec b\times\vec c)\bigg)\bigg((\vec a\times\vec b)\cdot\vec c\bigg)=1$$

$$\bigg(\vec a\cdot(\vec b\times\vec c)\bigg)^2=1$$

$$\vec a\cdot(\vec b\times\vec c)=\pm1$$