Let $\vec{P}, \vec{Q}$ and $\vec{R}$ be three non-zero vectors in the three dimensional right handed rectangular coordinate system. Then

• Correct answer
  A

  if $\vec{P}, \vec{Q}$ and $\vec{P}+\vec{Q}$ are unit vectors then $|\vec{P}-\vec{Q}|=\frac{\sqrt{3}}{2}$.
• Correct answer
  B

  the vectors $\vec{P} \times(\vec{Q} \times \vec{R}), \vec{Q} \times(\vec{R} \times \vec{P})$ and $\vec{R} \times(\vec{P} \times \vec{Q})$ are coplanar.
• C

  if $\vec{P} \times \vec{Q}=\vec{R}$ and $\vec{Q} \times \vec{R}=\vec{P}$ then $\vec{P}, \vec{Q}$ and $\vec{R}$ are orthogonal in pairs and $|\vec{P}|=|\stackrel{\rightharpoonup}{R}|$
• D

  if $\vec{P}, \vec{Q}$ and $\vec{R}$ are unit vectors then the angle between $\vec{P}+\vec{Q}+\vec{R}$ and any of $\vec{P}, \vec{Q}$ and $\vec{R}$ is the same.

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