What is the cross product of vectors A = (1, 2, 3) and B = (4, 5, 6)?

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Question: What is the cross product of vectors A = (1, 2, 3) and B = (4, 5, 6)?

Options:

Correct Answer: (-3, 6, -3)

Solution:

Cross product A × B = |i  j  k| |1  2  3| |4  5  6| = (-3, 6, -3).

What is the cross product of vectors A = (1, 2, 3) and B = (4, 5, 6)?

What is 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 and the components of A and B.
Step 3: Write the determinant as a 3x3 matrix: |i j k| |1 2 3| |4 5 6|.
Step 4: Calculate the determinant by expanding it. This involves calculating the components for i, j, and k.
Step 5: For the i component, calculate (2*6 - 3*5) = 12 - 15 = -3.
Step 6: For the j component, calculate (1*6 - 3*4) = 6 - 12 = -6, but remember to change the sign, so it becomes +6.
Step 7: For the k component, calculate (1*5 - 2*4) = 5 - 8 = -3.
Step 8: Combine the components to get the final result: A × B = (-3, 6, -3).

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