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For vectors A = 2i + j and B = 3i + 4j, what is the scalar product A · B?

Practice Questions

Q1
For vectors A = 2i + j and B = 3i + 4j, what is the scalar product A · B?
  1. 14
  2. 10
  3. 12
  4. 8

Questions & Step-by-Step Solutions

For vectors A = 2i + j and B = 3i + 4j, what is the scalar product A · B?
  • Step 1: Identify the components of vector A. A = 2i + j means A has a component of 2 in the i direction and 1 in the j direction.
  • Step 2: Identify the components of vector B. B = 3i + 4j means B has a component of 3 in the i direction and 4 in the j direction.
  • Step 3: Multiply the i components of A and B together. This is (2)(3) = 6.
  • Step 4: Multiply the j components of A and B together. This is (1)(4) = 4.
  • Step 5: Add the results from Step 3 and Step 4 together. This is 6 + 4 = 10.
  • Step 6: The scalar product A · B is 10.
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