Let $\hat{i}, \hat{j}, \hat{k}$ be three mutually orthogonal unit vectors and let $x, y, z$ be three distinct real numbers. If the vectors $\vec{u}=x \hat{i}+y \hat{j}+z \hat{k}, \vec{v}=y \hat{i}+z \hat{j}+x \hat{k}$ and $\vec{w}=z \hat{i}+x \hat{j}+y \hat{k}$ are coplanar then

• Correct answer
  A

  $\vec{u}+\vec{v}+\vec{w}=\overrightarrow{0}$, where $\overrightarrow{0}$ is the null vector.
• Correct answer
  B

  $\hat{i}+\hat{j}+\hat{k}$ is normal to the plane containing $\vec{u}, \vec{v}$ and $\vec{w}$.
• Correct answer
  C

  the angle between any two of the vectors $\vec{v}, \vec{v}$ and $\vec{w}$ is $120^{\circ}$.
• Correct answer
  D

  $\vec{u} \times \vec{v}=\vec{v} \times \vec{w}=\vec{w} \times \vec{u}$.

Hence, the correct answer is options: 'A', 'B', 'C', 'D'.