Find the cross product of vectors A = (1, 2, 3) and B = (4, 5, 6).

Find the cross product of vectors A = (1, 2, 3) and B = (4, 5, 6).

Step 1: Write down the vectors A and B. A = (1, 2, 3) and B = (4, 5, 6).
Step 2: Set up the determinant for the cross product using the unit vectors i, j, k.
Step 3: Create a 3x3 matrix with the first row as the unit vectors (i, j, k), the second row as the components of vector A, and the third row as the components of vector B.
Step 4: The matrix looks like this: | i j k | | 1 2 3 | | 4 5 6 |.
Step 5: Calculate the determinant of this matrix. This involves finding the determinant using the formula: i*(2*6 - 3*5) - j*(1*6 - 3*4) + k*(1*5 - 2*4).
Step 6: Simplify each part: i*(-3) - j*(-6) + k*(-3).
Step 7: Combine the results to get the final vector: (-3, 6, -3).

Cross Product – The cross product of two vectors in three-dimensional space results in a vector that is perpendicular to both original vectors.
Determinants – The calculation of the cross product involves the determinant of a 3x3 matrix formed by the unit vectors and the components of the vectors.