Question

If $\overline{a},\overline{b},\overline{c}$ are non-coplanar vectors such that $\overline{a}\times \overline{b}=\overline{c},\overline{b}\times \overline{c}=\overline{a},\overline{c}\times \overline{a}=\overline{b}$, then $|\overline{a}|+2|\overline{b}|-3|\overline{c}|$ is equal to

• A. $1$
• B. $0$
• C. $2$
• D. $3$

Answer 1

Answer: (B)

$0$

The given condition is possible only when all three vectors $\overline{a},\overline{b},\overline{c}$ are unit vectors, and that also they are mutually perpendicular to each other.
Thus, $|\overline{a}|+2|\overline{b}|-3|\overline{c}|=1+2-3=0.$