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For vectors A = (3, -2, 1) and B = (1, 4, -2), find A · B.

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Question: For vectors A = (3, -2, 1) and B = (1, 4, -2), find A · B.

Options:

  1. -1
  2. 0
  3. 1
  4. 2

Correct Answer: -1

Solution: 

A · B = 3*1 + (-2)*4 + 1*(-2) = 3 - 8 - 2 = -7.

For vectors A = (3, -2, 1) and B = (1, 4, -2), find A · B.

Practice Questions

Q1
For vectors A = (3, -2, 1) and B = (1, 4, -2), find A · B.
  1. -1
  2. 0
  3. 1
  4. 2

Questions & Step-by-Step Solutions

For vectors A = (3, -2, 1) and B = (1, 4, -2), find A · B.
  • Step 1: Identify the components of vector A, which are (3, -2, 1).
  • Step 2: Identify the components of vector B, which are (1, 4, -2).
  • Step 3: Multiply the first components of A and B: 3 * 1 = 3.
  • Step 4: Multiply the second components of A and B: -2 * 4 = -8.
  • Step 5: Multiply the third components of A and B: 1 * -2 = -2.
  • Step 6: Add the results from Steps 3, 4, and 5 together: 3 + (-8) + (-2).
  • Step 7: Calculate the sum: 3 - 8 = -5, then -5 - 2 = -7.
  • Step 8: The final result of A · B is -7.
  • Dot Product of Vectors – The dot product is calculated by multiplying corresponding components of two vectors and summing the results.
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