If a , b , c are three vectors such that a ( b + c )+ b ( c + a )+ c ( a + b )=0 and | a |=1 , | b |=8 and | c |=4 , then | a + b + c | has the value

Step-by-step solution

aligned & | a |=1,| b |=8,| c |=4, and & a ( b + c )+ b ( c + a )+ c ( a + b )=0 & 2( a b + b c + c a )=0 aligned Now, aligned & | a + b + c |^2=| a |^2+| b |^2+| c |^2+2( a b + b c + c a ) & | a + b + c |^2=1+64+16+0 [ From (i) ] & | a + b + c |^2=81 & | a + b + c |=9 aligned