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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)?
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Practice Questions
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Q1
What is the cross product of vectors A = (1, 2, 3) and B = (4, 5, 6)?
(-3, 6, -3)
(0, 0, 0)
(3, -6, 3)
(1, -2, 1)
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Cross product A × B = |i j k| |1 2 3| |4 5 6| = (-3, 6, -3).
Questions & Step-by-step Solutions
1 item
Q
Q: What is the cross product of vectors A = (1, 2, 3) and B = (4, 5, 6)?
Solution:
Cross product A × B = |i j k| |1 2 3| |4 5 6| = (-3, 6, -3).
Steps: 8
Show Steps
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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