Question

If $\overline{a},\overline{b},\overline{c}$ are three vectors such that $|\overline{a}|=1,|\overline{b}|=2,|\overline{c}|=3$, and $\overline{a}.\overline{b}=\overline{b}.\overline{c}=\overline{c}.\overline{a}=0$, then $|\left[\overline{a}\overline{b}\overline{c}\right]|=$

• A. $0$
• B. $2$
• C. $3$
• D. $6$

Answer 1

The correct option is D $6$

Using

$|\left[\overline{a}\overline{b}\overline{c}\right]{|}^2=\left|\begin{array}{ccc}\overline{a}.\overline{a}& \overline{a}.\overline{b}& \overline{a}.\overline{c}\\ \overline{b}.\overline{a}& \overline{b}.\overline{b}& \overline{b}.\overline{c}\\ \overline{c}.\overline{a}& \overline{c}.\overline{b}& \overline{c}.\overline{c}\end{array}\right|=\left|\begin{array}{ccc}1& 0& 0\\ 0& 4& 0\\ 0& 0& 9\end{array}\right|=36$, Use the given values

$\Rightarrow |\left[\overline{a}\overline{b}\overline{c}\right]|=\pm 6$