Let a , b and c be vectors of magnitude 2,3 and 4 respectively. If a is perpendicular to ( b + c ), b is perpendicular to ( c + a ) and c is perpendicular to ( a + b ) , then the magnitude of a + b + c is equal to

Step-by-step solution

aligned & a ( b + c ), b ( c + a ) and c ( a + b ) & a b + a c =0, ~b c + b a =0, c a + c b =0 & a b + b c + c a =0 aligned aligned | a + b + c |^2 & =| a |^2+| b |^2+| c |^2+2( a b + b c + c a ) & =2^2+3^2+4^2+2(0) & =4+9+16 aligned array ll & | a + b + c |^2=29 & | a + b + c |= 29 array