COMEDK2015MathematicsVector Algebra
If a, be are three non-zero vectors such that each one of them are perpendicular to the sum of the other two vectors, then the value of a + b + c ² is
Options
- A|a|²+|b|²+ q²
- Bà +|b|+| d |
- C2 (| a |²+|b|²+ d² )
- D1 2 (|a|²+|b|²+ d² )
Correct answer
A. |a|²+|b|²+ q²
Step-by-step solution
According to the question, a (b+c)=0, b ( c + a )=0, c ( a + b )=0 a b+a c=0 ...(i) b. c+b a=0 ...(ii) c a +c b=0 ...(iii) Adding Eqs. (i), (ii) and (iii), we get 2( a b + b c + c . a )=0 ...(iv) Now, a+b+c²=| a |²+| b |²+ c ²+2( a b + b c + c a )=| a |²+| b |²+| c |² [using Eq. (iv)]