Question

If $a.b=b.c=c.a=0,$ then $a.(b\times c)$ is equal to

• A. a lion-zero vector
• B. 1
• C. $-1$
• D. $|a||b||c|$

Answer 1

Answer: (D)

$a.(b\times c)=|a|b\times c|\cos \theta ,\theta =0$ or $\pi$ ( $\because$ $a.b=b.c=c.a=0,$ therefore, a,b,c are mutually at right angles and hence $b\times c$ is parallel to a)
$\therefore$ $a.(b\times c)=|a|(|b||c|\sin 90{}^{\circ })$ $=|a||b||c|$