a , b , c are three vectors such that | a |=3 , | b |=5,| c |=7 . If a , b , c are perpendicular to the vectors b + c , c + a , a + b respectively, then ( a + b + c )^2-2 =

Step-by-step solution

We have, | a |=3,| b |=5,| c |=7 a is perpendicular to ( b + c ) and b is perpendicular to c + a So, b ( c + a )=0 and c is perpendicular to ( a + b ) Adding Eqs. (i), (ii) and (iii), we get Now, | a + b + c |^2 aligned & =| a |^2+| b |^2+| c |^2+2( a b + b c + c a ) & =(3)^2+(5)^2+(7)^2+0=83 aligned Now, ( a + b + c )^2-2 = 83-2 = 81 =9