Question

If a vector $\vec{\alpha}$ lie in the plane of $\vec{\beta}$ and $\vec{\gamma}$ then which is correct?

• A. $[\vec{\alpha} \vec{\beta}\vec{\gamma}]=0$
• B. $[\vec{\alpha} \vec{\beta}\vec{\gamma}]=1$
• C. $[\vec{\alpha} \vec{\beta}\vec{\gamma}]=3$
• D. $[\vec{\beta} \vec{\gamma} \vec{\alpha} ]=1$

Answer 1

Answer: (A)

If vector $\vec{\alpha}$ lie in the plane of $\vec{\beta}$ and $\vec{\gamma}$ then all three vectors $\vec{\alpha}, \vec{\beta}$ and $\vec{\gamma}$ are coplanar.
For three vectors to be coplanar, their scalar triple product must be zero
i.e. $\left[\vec{\alpha} \,\vec{\beta} \, \vec{\gamma} \right]=0$