Question

If $\overline{a},\overline{b},\overline{c}$ are mutually perpendicular vectors having magnitudes $1,2,3$ respectively, then find $\begin{array}{c}\left[(\overline{a}+\overline{b}+\overline{c}).(\overline{b}\times \overline{a})\right]\times \overline{c}\end{array}$

• A. $0$
• B. $6$
• C. $12$
• D. $18$

Answer 1

The correct option is A $0$

We have,

$\begin{array}{c}\left[(\overline{a}+\overline{b}+\overline{c}).(\overline{b}\times \overline{a})\right]\times \overline{c}\\ \left[(\overline{a}\times \overline{b})-(\overline{a}\times \overline{a})+(\overline{b}\times \overline{b})-(\overline{b}\times \overline{a})+(\overline{c}\times \overline{b})-(\overline{c}\times \overline{a})\right]\times \overline{c}\end{array}$

$if,\overline{a}\times \overline{a}=1,\overline{a}\times \overline{b}=0$

= $\left[0-1+1-0+1-0\right]\times \overline{c}$

$=0$

So, the correct option is A.