If is angle between the vectors a and b where | a |=4, | b |=3 and ( 4 , 3 ) , then |( a - b ) ( a + b )|^2+4( a b )^2 has the value

Step-by-step solution

aligned & |( a - b ) ( a + b )|^2+4( a b )^2 & =|( a a )+( a b )-( b a )-( b b )|^2+4( a b )^2 & =|( a b )-( b a )|^2+4( a b )^2 & =|2( a b )|^2+4( a b )^2 [( a b )=-( b a )] & =4|( a b )|^2+4( a b )^2 & =4 [| a b |^2+( a b )^2 ] & =4| a |^2| b |^2 & =4(4)^2(3)^2 & =576 aligned