Answer: (a.c)(b.d) - (a.d)(b.c).
- A (a.b)(c.d)
- B (a x c).(b x d)
- C (a.c)(b.d) - (a.d)(b.c)
- D (a.d)(b.c) - (a.c)(b.d)
Correct answer: C. (a.c)(b.d) - (a.d)(b.c)
Explanation: Using the scalar quadruple product identity (Lagrange): (a×b)·(c×d) = det[[a·c, a·d],[b·c, b·d]] = (a·c)(b·d) − (a·d)(b·c). Answer: (a·c)(b·d) − (a·d)(b·c).
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