If a and b are two unit vectors such that c =( a c )+ b , then the maximum value of [ a b c ] is

Step-by-step solution

aligned & c =( a c )+ b & | c |^2=| a + c |^2+| b |^2+2( a c ) b & 2[ a b c ]=| a c |^2+1-| c |^2 aligned Let angle between vectors a and c is ' '. So, [ array lll a & b & c array ]= 1 2 [| c |^2 ^2 -| c |^2+1 ] From Eq. (i) and (ii) aligned & 1 2 1-| c |^2 ^2 =| c |^2 ^2 | c |^2= 1 ^2 +2 ^2 & [ array lll a & b & c array ]=| c |^2 ^2 = ^2 ^2 +2 ^2 = ^2 1+ ^2 & = 1 cosec ^2 +1 & aligned For maximum value of [ array lll a & b & c array ], cosec ^2 =1 , so [ array lll a & b & c array ]_ = 1 2