Let $\vec{a}, \vec{b}, \vec{c}$ be three non-coplanar vectors in the three dimensional $x y z$-space. Which of the following vector(s) lies (lie) in the plane containing $\vec{a}$ and $\vec{b}$ ?
(i) $(\vec{a} \times \vec{b}) \times \vec{a}$
(ii) $(\vec{a} \times \vec{b}) \times \vec{b}$;
(iii) $(\vec{a} \times \vec{b}) \times \vec{c}$.

• A

  (i) only
• B

  (i) and (ii) only
• C

  (iii) only
• Correct answer
  D

  (i), (ii) and (iii)

Hence, the correct answer is option: 'D'.