• # question_answer Direction: Let a, b and c are three non-coplanar vectors, i.e., $[a\,b\,c]\,\ne 0$. The three new vectors $a',\,\,b'$ and c' defined by the equation $a'=\frac{b\times c}{[a\,\,b\,\,c]},\,\,b'=\frac{c\times a}{[a\,\,b\,\,c]}$and$c'=\frac{a\times b}{[a\,\,b\,\,c]}$ are called reciprocal system to the vectors a, b and c. If a, b, c and a', b', c' are reciprocal system of vectors, then the value of$a\times a'+b\times b'+c\times c'$ is A)  $a\times a'+b\times b'+c\times c'$    B)  $2\,(a'\times b'\times c')$ C)  $\frac{[a\,\,b\,\,c]}{2}$ D)  0

$\therefore \,\,a\times a'+b\times b'+c+c'$$=\frac{1}{[a\,b\,c]}[a\times (b\times c)+b\times (c\times a)+c\times (a\times b)]$(for cyclic order) $=\frac{1}{[a\,b\,c]}[0]=0$