Question

Let $\overline{a},\overline{b},\overline{c}$ be three vectors such that $\overline{a}\times \overline{b}=\overline{c}$ and $\overline{c}\times \overline{a}=\overline{b}$, then

• A. $\overline{a}.\overline{b}=|\overline{c}{|}^2$
• B. $\overline{c}.\overline{a}=|\overline{b}{|}^2$
• C. $\overline{b}.\overline{c}=|\overline{a}{|}^2$
• D. $\overline{a}\parallel \overline{b}\times \overline{c}$

Answer 1

The correct option is D $\overline{a}\parallel \overline{b}\times \overline{c}$

$\overline{a}\times \overline{b}=\overline{c}$ and $\overline{c}\times \overline{a}=\overline{b}$
$\Rightarrow \overline{c}\perp \overline{b},\overline{a}$ and $\overline{b}\perp \overline{c},\overline{a}$
$\Rightarrow \overline{a}$ is perpendicular to $\overline{b}$ and $\overline{c}$
$\Rightarrow \overline{a}||\overline{b}\times \overline{c}$