Question

Let the vector $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ and $\overrightarrow{d}$ be such that $\left(\overrightarrow{a}\times \overrightarrow{b}\right)\times \left(\overrightarrow{c}\times \overrightarrow{d}\right)=0$. Let $P_1$ and $P_2$ be planes determined by the pairs of vectors $\overrightarrow{a},\overrightarrow{b}$ and $\overrightarrow{c},\overrightarrow{d}$ respectively then the angle between $P_1$ and $P_2$ is

• A. $0$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{3}$
• D. $\frac{\pi }{2}$

Answer 1

The correct option is A $0$

$P1planeisdeterminedby\overline{a}and\overline{b}.$

$P2planeisdeterminedby\overline{c}and\overline{d}.$

$and(\overline{a}\times \overline{b})\times (\overline{c}\times \overline{d})=0$

$⟹NormaltwoplanesP1andP2$

$areparallel,$

$HenceplanesP1andP2areparallel,$

$\therefore AnglebetweenP1andP2=0.$