Question

If $\overrightarrow{a}$, $\overrightarrow{b}$, $\overrightarrow{c}$ and $\overrightarrow{d}$ are coplanar vectors then ($\overrightarrow{a}$ $\times \overrightarrow{c}$) $\times$ ($\overrightarrow{b}$ $\times$ $\overrightarrow{d}$)

• A. $1$
• B. $\overrightarrow{a}$
• C. $\overrightarrow{b}$
• D. $\overrightarrow{0}$

Answer 1

The correct option is D $\overrightarrow{0}$

$\because \overline{a},\overline{b},\overline{c}\&\overline{d}arecoplanar.$

$\therefore (\overline{a}\times \overline{b})and(\overline{c}\times \overline{d})$ will both represent the normal to the plane on which $\overline{a},\overline{b},\overline{c}\&\overline{d}$ are lying.

Hence,angle between $(\overline{a}\times \overline{b})$ and $(\overline{c}\times \overline{d})$ will be $0$ i.e.,they will be parallel or anti-parallel.

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