Answer: -(|a| 2 +|b| 2 +|c| 2 )/2.
- A 0
- B (|a|<sup>2</sup>+|b|<sup>2</sup>+|c|<sup>2</sup>)/2
- C -(|a|<sup>2</sup>+|b|<sup>2</sup>+|c|<sup>2</sup>)/2
- D |a|<sup>2</sup>+|b|<sup>2</sup>+|c|<sup>2</sup>
Correct answer: C. -(|a|<sup>2</sup>+|b|<sup>2</sup>+|c|<sup>2</sup>)/2
Explanation: |a+b+c|<sup>2</sup> = 0. Expanding: |a|<sup>2</sup>+|b|<sup>2</sup>+|c|<sup>2</sup>+2(a.b+b.c+c.a) = 0. So a.b+b.c+c.a = -(|a|<sup>2</sup>+|b|<sup>2</sup>+|c|<sup>2</sup>)/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