📐 Mathematics · Vector Algebra · JEE

If a + b + c = 0, then a.b + b.c + c.a =

Answer: -(|a|²+|b|²+|c|²)/2.

Correct answer: C. -(|a|²+|b|²+|c|²)/2

Explanation: |a+b+c|² = 0. Expanding: |a|²+|b|²+|c|²+2(a.b+b.c+c.a) = 0. So a.b+b.c+c.a = -(|a|²+|b|²+|c|²)/2.

Triangle law of vector addition: placing vector b at the head of vector a, the diagonal from the start to the final head gives the resultant a + b.

Concept context

Vectors, dot product, cross product, and geometric applications