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If A = 4i + 2j and B = -i + 3j, what is the scalar triple product A · (B × A)? (
If A = 4i + 2j and B = -i + 3j, what is the scalar triple product A · (B × A)? (2023)
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If A = 4i + 2j and B = -i + 3j, what is the scalar triple product A · (B × A)? (2023)
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B × A = |i j k| |-1 3 0| |4 2 0| = 0, hence A · (B × A) = 0.
Questions & Step-by-step Solutions
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Q: If A = 4i + 2j and B = -i + 3j, what is the scalar triple product A · (B × A)? (2023)
Solution:
B × A = |i j k| |-1 3 0| |4 2 0| = 0, hence A · (B × A) = 0.
Steps: 8
Show Steps
Step 1: Identify the vectors A and B. A = 4i + 2j and B = -i + 3j.
Step 2: Write down the formula for the cross product B × A.
Step 3: Set up the determinant for the cross product using the unit vectors i, j, k and the components of B and A.
Step 4: Calculate the determinant: |i j k| |-1 3 0| |4 2 0|.
Step 5: Compute the determinant to find B × A. The result is (0i + 0j + 10k) = 10k.
Step 6: Now, find the dot product A · (B × A). Since B × A = 10k, we need to calculate A · (10k).
Step 7: The dot product A · (10k) is 0 because A has no k component (A = 4i + 2j).
Step 8: Therefore, A · (B × A) = 0.
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