Let a and c be unit vectors at an angle 3 with each other. If ( a ( b c )) ( a c )=5 , then [ array lll a & b & c array ]=

Step-by-step solution

The given equation is ( a ( b c )) ( a c ) = 5 . Using the BAC-CAB identity, a ( b c ) = ( a c ) b - ( a b ) c . Substituting into the original equation yields [( a c ) b - ( a b ) c ] ( a c ) = 5 . Expanding the dot product gives ( a c )[ b ( a c )] - ( a b )[ c ( a c )] = 5 . Since c ( a c ) = 0 (as two identical vectors in a scalar triple product yield zero), the second term vanishes, simplifying to ( a c )[ b ( a c )] = 5 . Given a and c are unit vectors with an angle of 3 , a c = 1 1 3 = 1 2 . Substituting, 1