Question

Two planes are perpendicular to one another one of them contains vectors $\overrightarrow{a},\overrightarrow{c}$ and other contains $\overrightarrow{b},\overrightarrow{d}$ then $(\overrightarrow{a}\times \overrightarrow{c}).(\overrightarrow{b}\times \overrightarrow{d})=$

• A. $1$
• B. $0$
• C. $-1$
• D. none of these

Answer 1

Answer: (B)

$0$

${\overrightarrow{n}}_1$ & ${\overrightarrow{n}}_2$ are 2 normal vector from plane 1 & plane 2 respectively
${\overrightarrow{n}}_1=\overrightarrow{a}\times \overrightarrow{c}$
${\overrightarrow{n}}_2=\overrightarrow{b}\times \overrightarrow{d}$
As two planes are $\perp$ to each other than $n_1$ & $n_2$ are $\perp$ to each other
$\overrightarrow{n_1}\cdot \overrightarrow{n_2}=0$
$(\overrightarrow{a}\times \overrightarrow{c}).(\overrightarrow{b}\times \overrightarrow{d})=0$