If A = 7i + 1j and B = 1i + 7j, find A · B.

Practice Questions

Q1
If A = 7i + 1j and B = 1i + 7j, find A · B.
  1. 56
  2. 14
  3. 8
  4. 50

Questions & Step-by-Step Solutions

If A = 7i + 1j and B = 1i + 7j, find A · B.
  • Step 1: Identify the components of vector A, which are 7i and 1j.
  • Step 2: Identify the components of vector B, which are 1i and 7j.
  • Step 3: Multiply the i components of A and B together: 7 (from A) * 1 (from B) = 7.
  • Step 4: Multiply the j components of A and B together: 1 (from A) * 7 (from B) = 7.
  • Step 5: Add the results from Step 3 and Step 4 together: 7 + 7 = 14.
  • Step 6: The final result of A · B is 14.
  • Dot Product – The dot product of two vectors A and B is calculated by multiplying their corresponding components and summing the results.
  • Vector Components – Understanding how to break down vectors into their i (x-axis) and j (y-axis) components is essential for calculating the dot product.
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