Question Detail

First compute B × C. B = 3i + 0j - 3k, C = 6i + 0j - 4k. B × C = determinant |i j k; 3 0 -3; 6 0 -4| = i(0×(-4) - (-3)×0) - j(3×(-4) - (-3)×6) + k(3×0 - 0×6) = i(0 - 0) - j(-12 + 18) + k(0) = -j(6) = -6j. Then A × (B × C) = A × (-6j) = -6 (A × j). A × j = (4i + 0j + 2k) × j = 4(i×j) + 2(k×j) = 4k + 2(-i) = -2i + 4k. Multiply by -6: 12i - 24k. Not matching. If I did B×C correctly: B×C = (0×(-4) - (-3)×0)i - (3×(-4) - (-3)×6)j + (3×0 - 0×6)k = (0 - 0)i - (-12 + 18)j + (0 - 0)k = -6j. Yes. Then A×(-6j) = -6(A×j). A×j = (4i+2k)×j = 4(i×j) + 2(k×j) = 4k + 2(-i) = -2i + 4k. Times -6 = 12i - 24k. Option B is -72i + 24k, which is different. Maybe B and C have j components? If B = 3i - 3k means no j, correct. Possibly I misread A: A = 4i + 2k, so no j. Result 12i - 24k not in options. If A had j component, result might match.