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

Practice Questions

Q1
If A = 7i + 1j and B = 1i + 7j, calculate A · B.
  1. 56
  2. 58
  3. 60
  4. 62

Questions & Step-by-Step Solutions

If A = 7i + 1j and B = 1i + 7j, calculate A · B.
  • Step 1: Identify the components of vector A. A = 7i + 1j means A has a component of 7 in the i direction and 1 in the j direction.
  • Step 2: Identify the components of vector B. B = 1i + 7j means B has a component of 1 in the i direction and 7 in the j direction.
  • Step 3: To calculate the dot product A · B, use the formula: A · B = (A's i component) * (B's i component) + (A's j component) * (B's j component).
  • Step 4: Substitute the values into the formula: A · B = (7) * (1) + (1) * (7).
  • Step 5: Calculate the first part: (7) * (1) = 7.
  • Step 6: Calculate the second part: (1) * (7) = 7.
  • Step 7: Add the results from Step 5 and Step 6: 7 + 7 = 14.
  • Dot Product – The dot product of two vectors is calculated by multiplying their corresponding components and summing the results.
  • Vector Representation – Understanding how to represent vectors in terms of their components along the i and j axes.
Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely