Question

If $\overline{a},\overline{b},\overline{c}$ form a left handed orthogonal system and $\overline{a}\cdot \overline{a}=4,\overline{b}\cdot \overline{b}=9,\overline{c}\cdot \overline{c}$=16 then $\left[\overline{a}\overline{b}\overline{c}\right]$ =

• A. 24
• B. -24
• C. 12
• D. -12

Answer 1

The correct option is B

-24

${\left[\overline{a}\overline{b}\overline{c}\right]}^2$ =$\left|\begin{array}{ccc}\overline{a}\cdot \overline{a}& \overline{a}\cdot \overline{b}& \overline{a}\cdot \overline{c}\\ \overline{b}\cdot \overline{a}& \overline{b}\cdot \overline{b}& \overline{b}\cdot \overline{c}\\ \overline{c}\cdot \overline{a}& \overline{c}\cdot \overline{b}& \overline{c}\cdot \overline{c}\end{array}\right|$ = $\left|\begin{array}{ccc}4& 0& 0\\ 0& 9& 0\\ 0& 0& 16\end{array}\right|$

$\left[\overline{a}\overline{b}\overline{c}\right]=-24$