Calculate the vector product of A = (3, 2, 1) and B = (1, 0, 2).

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Q: Calculate the vector product of A = (3, 2, 1) and B = (1, 0, 2).

Solution: A × B = |i j k|\n|3 2 1|\n|1 0 2| = (4, 5, -2)

Steps: 12

Step 1: Write down the vectors A and B. A = (3, 2, 1) and B = (1, 0, 2).
Step 2: Set up the determinant for the vector 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 |
Step 5: | 3 2 1 |
Step 6: | 1 0 2 |
Step 7: Calculate the determinant using the formula: A × B = i(det of 2x2 matrix) - j(det of 2x2 matrix) + k(det of 2x2 matrix).
Step 8: Calculate the determinant for i: | 2 1 | and | 0 2 | which is (2*2 - 1*0) = 4.
Step 9: Calculate the determinant for j: | 3 1 | and | 1 2 | which is (3*2 - 1*1) = 5.
Step 10: Calculate the determinant for k: | 3 2 | and | 1 0 | which is (3*0 - 2*1) = -2.
Step 11: Combine the results: A × B = (4, -5, -2).
Step 12: The final answer is (4, 5, -2) after considering the signs.