a, b and c are 3 vectors, such that a + b + c = 0, |a| = 1, |b| = 2|c|

• Vectors

a, b and c are 3 vectors, such that a + b + c = 0, |a| = 1, |b| = 2|c|, then a.b + b.c + c.a is equal to

1. 1
2. 0
3. -7
4. 7

Solution

a + b + c = 0, (a+b+c)(a+b+c) = 0

|a|² + |b|² + |c|² + 2(a.b + b.c +c.a) = 0

The correct option is C.