Answer: |a| 2 |b| 2 - (a.b) 2.
- A (a.b)<sup>2</sup>
- B |a|<sup>2</sup>|b|<sup>2</sup> + (a.b)<sup>2</sup>
- C |a|<sup>2</sup>|b|<sup>2</sup> - (a.b)<sup>2</sup>
- D |a|<sup>2</sup> - |b|<sup>2</sup>
Correct answer: C. |a|<sup>2</sup>|b|<sup>2</sup> - (a.b)<sup>2</sup>
Explanation: Lagrange identity: |a x b|<sup>2</sup> = |a|<sup>2</sup>|b|<sup>2</sup> - (a.b)<sup>2.</sup> This follows since |a x b| = |a||b|sin(theta) and (a.b) = |a||b|cos(theta).
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