Step 1: Identify the components of vector A and vector B. Vector A = 3i + 4j means A has components (3, 4, 0) and vector B = 4i + 3j means B has components (4, 3, 0).
Step 2: Set up the determinant for the cross product using the unit vectors i, j, k and the components of A and B. This looks like: |i j k| |3 4 0| |4 3 0|.
Step 3: Calculate the determinant. The formula for the determinant is: i*(4*0 - 0*3) - j*(3*0 - 0*4) + k*(3*3 - 4*4).
Step 4: Simplify each part. The i component is (4*0 - 0*3) = 0, the j component is (3*0 - 0*4) = 0, and the k component is (3*3 - 4*4) = 9 - 12 = -3.
Step 5: Combine the results. The cross product A × B = 0i - 0j - 3k, which simplifies to -3k.
