Question

If $(\vec{a} \times \vec{b}) \times(\vec{c} \times \vec{d}) \cdot(\vec{a} \times \vec{d})=0$, then which of the following is always true?

• A. $\vec{a}, \vec{b}, \vec{c}, \vec{d}$ are necessarily coplanar
• B. either $\vec{a}$ or $\vec{d}$ must lie in the plane of $\vec{b}$ and $\vec{c}$
• C. either $\vec{b}$ or $\vec{c}$ must lie in the plane of $\vec{a}$ and $\vec{d}$
• D. either $\vec{a}$ or $\vec{b}$ must lie in the plane of $\vec{c}$ and $\vec{d}$

Answer 1

Answer: (A)

$(\vec{a} \times \vec{b}) \times(\vec{c} \times \vec{d}) \cdot(\vec{a} \times \vec{d})=0$
then $\vec{a}, \vec{b}, \vec{c}, \vec{d}$ are neccessarily colpanar