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Calculate the scalar product of the vectors A = (4, -1, 2) and B = (2, 3, 1).
Calculate the scalar product of the vectors A = (4, -1, 2) and B = (2, 3, 1).
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Q1
Calculate the scalar product of the vectors A = (4, -1, 2) and B = (2, 3, 1).
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8
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A · B = 4*2 + (-1)*3 + 2*1 = 8 - 3 + 2 = 7.
Questions & Step-by-step Solutions
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Q
Q: Calculate the scalar product of the vectors A = (4, -1, 2) and B = (2, 3, 1).
Solution:
A · B = 4*2 + (-1)*3 + 2*1 = 8 - 3 + 2 = 7.
Steps: 7
Show Steps
Step 1: Identify the components of vector A, which are (4, -1, 2).
Step 2: Identify the components of vector B, which are (2, 3, 1).
Step 3: Multiply the first component of A (4) by the first component of B (2). This gives 4 * 2 = 8.
Step 4: Multiply the second component of A (-1) by the second component of B (3). This gives -1 * 3 = -3.
Step 5: Multiply the third component of A (2) by the third component of B (1). This gives 2 * 1 = 2.
Step 6: Add the results from Steps 3, 4, and 5 together: 8 + (-3) + 2.
Step 7: Calculate the sum: 8 - 3 + 2 = 7.
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