Answer: 2(|a| 2 + |b| 2 ).
- A 2|a|<sup>2</sup>
- B 2|b|<sup>2</sup>
- C 2(|a|<sup>2</sup> + |b|<sup>2</sup>)
- D 4(|a|<sup>2</sup> + |b|<sup>2</sup>)
Correct answer: C. 2(|a|<sup>2</sup> + |b|<sup>2</sup>)
Explanation: Parallelogram law of cosines: |a+b|<sup>2</sup> + |a-b|<sup>2</sup> = 2(|a|<sup>2</sup> + |b|<sup>2</sup>). The sum of squares of diagonals equals twice the sum of squares of the sides.
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