Passage: Let a b = c and b c = a . Question: Consider the following statements : I. ( a b ) c +( b c ) a =( c a ) b II. ( a b ) ( b c ) b =1 Which of the statements given above is/are correct ?

Step-by-step solution

Given a b = c and b c = a . Taking the dot product of the first equation with c : ( a b ) c = c c [ a b c ] = | c |^2 Taking the dot product of the second equation with a : ( b c ) a = a a [ b c a ] = | a |^2 Using the properties of the scalar triple product, [ a b c ] = [ b c a ] = [ c a b ] . Thus, | a |^2 = | c |^2 = [ a b c ] . Evaluating Statement I: The left-hand side is ( a b ) c + ( b c ) a = [ a b c ] + [ b c a ] = 2[ a b c ] . The right-hand side is ( c a ) b = [ c a b ] = [ a b c ] . For the statement to