If a , b , c are three vectors such that a ( b + c ), b ( c + a ), and c ( a + b ) and | a | = 1, | b | = 2, | c | = 3 , then | a + b + c | is...

Step-by-step solution

Given a ( b + c ) , we have a ( b + c ) = 0 a b + a c = 0 Similarly, b ( c + a ) b ( c + a ) = 0 b c + b a = 0 And c ( a + b ) c ( a + b ) = 0 c a + c b = 0 Adding the above three equations, we get: 2( a b + b c + c a ) = 0 Using the identity for the square of the sum of three vectors: | a + b + c |^2 = | a |^2 + | b |^2 + | c |^2 + 2( a b + b c + c a ) Substituting the given values | a | = 1 , | b | = 2 , and | c | = 3 : | a + b + c |^2 = 1^2 + 2^2 + 3^2 + 0 | a + b + c |^2 = 1 + 4 + 9 = 14 | a + b + c | = 14 Answ