If a , b and c are three vectors such that | a |=3,| b |=4 and | c |=5 and a + b + c =0 , then a b is equal to

Step-by-step solution

aligned & a , b , c are three vectors such that | a |=3 , & array l | b |=4,| c |=5 and a + b + c =0 Now, a + b + c =0 a + b =- c array & aligned ( a + b )^2=(- c )^2 aligned & aligned & | a |^2+| b |^2+2 a b =| c |^2 [ a a =| a |^2 ] & 3^2+4^2+2 a b =5^2 & 2 a b =25-9-16 & 2 a b =0 & a b =0 aligned aligned