Answer: Perpendicular.
- A Parallel
- B Equal in magnitude
- C Perpendicular
- D Collinear
Correct answer: C. Perpendicular
Explanation: |a+b|<sup>2</sup> = |a-b|<sup>2</sup> gives |a|<sup>2</sup>+2a.b+|b|<sup>2</sup> = |a|<sup>2</sup>-2a.b+|b|<sup>2</sup>, so 4a.b = 0. Hence a.b = 0, meaning they are perpendicular.
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