If ( | a |=3,| b |=4,| c |=5 ) each one of ( a , b & c ) is perpendicular to the sum of the remaining then ( | a + b + c | ) is equal to

Step-by-step solution

Given that, each one of a , b and c is perpendicular to the sum of the remaining. So, a ( b + c )=0 (1) b | c + a |=0 (2) c a + b )=0 (3) Now, adding Eqs. (1), (2) and (3), we get 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=9+16+25 |a+ b + c |²=50 |a+ b + c |²=5 2