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If A = 6i + 8j and B = 2i + 3j, find the scalar product A · B.

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Question: If A = 6i + 8j and B = 2i + 3j, find the scalar product A · B.

Options:

  1. 42
  2. 54
  3. 48
  4. 36

Correct Answer: 48

Solution: 

A · B = (6)(2) + (8)(3) = 12 + 24 = 36.

If A = 6i + 8j and B = 2i + 3j, find the scalar product A · B.

Practice Questions

Q1
If A = 6i + 8j and B = 2i + 3j, find the scalar product A · B.
  1. 42
  2. 54
  3. 48
  4. 36

Questions & Step-by-Step Solutions

If A = 6i + 8j and B = 2i + 3j, find the scalar product A · B.
  • Step 1: Identify the components of vector A, which are 6i and 8j.
  • Step 2: Identify the components of vector B, which are 2i and 3j.
  • Step 3: Multiply the i components of A and B together: 6 (from A) * 2 (from B) = 12.
  • Step 4: Multiply the j components of A and B together: 8 (from A) * 3 (from B) = 24.
  • Step 5: Add the results from Step 3 and Step 4 together: 12 + 24 = 36.
  • Step 6: The scalar product A · B is 36.
  • Vector Operations – Understanding how to compute the scalar (dot) product of two vectors using their components.
  • Component Multiplication – Recognizing that the scalar product involves multiplying corresponding components of the vectors and summing the results.
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