Question Detail

First, find A × B. For 2D vectors, the cross product gives a scalar (the z-component). A × B = (2)(5) - (3)(3) = 10 - 9 = 1. Then (A × B) × C means multiply the scalar 1 by vector C, giving C itself: 4i-6j. But that's not among the options. If the notation means the vector triple product A × (B × C), we need to compute differently. B × C for 2D vectors is a scalar: (3)(-6) - (5)(4) = -18 - 20 = -38. Then A × (B × C) = A multiplied by the scalar -38 = -38(2i+3j) = -76i - 114j = -114i - 76j. This matches option A.