Answer: |a|2|b|2 - (a.b)2.
- A (a.b)2
- B |a|2|b|2 + (a.b)2
- C |a|2|b|2 - (a.b)2
- D |a|2 - |b|2
Correct answer: C. |a|2|b|2 - (a.b)2
Explanation: Lagrange identity: |a x b|2 = |a|2|b|2 - (a.b)2. 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