a , b , c are vectors such that | a |=5,| b |=4,| c |=3 and each is perpendicular to the sum of the other two, then | a + b + c |^2=

Step-by-step solution

We have a ( b + c )=0 b ( c + a )=0 and c ( a + b )=0 aligned & a b + a c =0 & b c + b a =0 & c a + c b =0 aligned From (1), (2) and (3), we get aligned & 2( a b + b c + c a )=0 & Now | a + b + c |^2=| a |^2+| b |^2+| c |^2+2( a b + b c + c a ) & | a + b + c |^2=(5)^2+(4)^2+(3)^2+2(0)=50 aligned