If a,b, c and a', b', c' are reciprocal system of vectors then fill in the blanks in the following :
(i) `a xx a' + b xx b' + c xx c' =` ........
(ii) `a' xx b' + b' xx c' + c' xx a' =` ........
(iii) `a.a' + b.b' + c.c' =`.........
`(iv) a'. (a +b) + b'. (b +c) +c'. (c +a) =` .......
(v) `(a + b + c). (a'+ b' + c') =` .......
(vi) `[abc] [a'b'c'] =` ........

Answer

(i) 0
(ii) `(a + b + c)/(|abc|)`
(iii) 3
(iv) 3
(v) 3
(vi) 1