Question

If $\overline{b}and\overline{c}$ are two non-collinear vectors such that $\overline{a}||(\overline{b}\times \overline{c})$, then $(\overline{a}\times \overline{b}).(\overline{a}\times \overline{c})$ is equal to

• A. $|\overline{a}{|}^2(\overline{b}.\overline{c})$
• B. $|\overline{b}{|}^2(\overline{a}.\overline{c})$
• C. $|\overline{c}{|}^2(\overline{a}.\overline{b})$
• D. $2|\overline{a}{|}^2(\overline{b}.\overline{c})$

Answer 1

The correct option is A $|\overline{a}{|}^2(\overline{b}.\overline{c})$

$\overline{a}\parallel (\overline{b}\times \overline{c})$

$\overline{a}=X(\overline{b}\times \overline{c})$

$(\overline{a}\times \overline{b})(\overline{a}\times \overline{c})=(\overline{a}\times \overline{a})(\overline{b}\cdot \overline{c})-0$

$={\left|\overline{a}\right|}^2(\overline{b}\cdot \overline{c})$