Given the vectors A = 2 i + 3 j + 4 k and B = 4 i + 3 j + 2 k , determine the cross product A B .

Step-by-step solution

The cross product of two vectors A and B is given by the determinant of their components: A B = vmatrix i & j & k 2 & 3 & 4 4 & 3 & 2 vmatrix Expanding the determinant along the first row: A B = i (3 2 - 4 3) - j (2 2 - 4 4) + k (2 3 - 3 4) A B = i (6 - 12) - j (4 - 16) + k (6 - 12) A B = -6 i + 12 j - 6 k