| 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. |
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
Correct Answer: D
Solution :
\[\therefore \,\,a\times a'+b\times b'+c+c'\]\[=\frac{1}{[a\,b\,c]}[a\times (b\times c)+b\times (c\times a)+c\times (a\times b)]\](for cyclic order) \[=\frac{1}{[a\,b\,c]}[0]=0\]
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