Question

If $(\overline{a},\overline{b})=\pi$, then $|4\overline{a}\times 5\overline{b}+\overline{b}\times \overline{a}|=$

• A. $0$
• B. $19|\overline{a}||\overline{b}|$
• C. $|\overline{a}||\overline{b}|$
• D. $2|\overline{a}||\overline{b}|$

Answer 1

The correct option is A $0$

$|4\overline{a}\times 5\overline{b}+\overline{b}\times \overline{a}|$
$=|20\overline{a}\times \overline{b}-\overline{a}\times \overline{b}|$
$=|19\overline{a}\times \overline{b}|$
$=19|\overline{a}||\overline{b}|\sin \pi$
$=0.$