Vectors i and b are such that | a |=1 ;| b |=4 and a b -2 . If c -2 a b -3 b , then the angle between b and c is

Step-by-step solution

aligned & Given: | a |=1,| b |=4 and a b =2 , & c =2 a b -3 b aligned Now that, | a b |^2=| a |^2| b |^2-| a b |^2 | a b |^2=16-4=12 Given that c =2 a b -3 b aligned & | c |^2=(2 a b -3 b )^2 & | c |^2=4| a b |^2+9| b |^2 aligned aligned & | c |^2=4(12)+9(16) & | c |^2=192 & | c |=8 3 aligned Now, b c = b (2 a b -3 b ) b c =-3| b |^2=-48 Angle between b and c is given by = ( b c ) (| b | c |) = -48 (4 8 3 ) = - 3 2 = ^4 ( - 3 2 ) = 5 6