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If the vectors A = 2i + 3j and B = 3i + 4j are perpendicular, what is the value

Practice Questions

Q1
If the vectors A = 2i + 3j and B = 3i + 4j are perpendicular, what is the value of A · B?
  1. 0
  2. 6
  3. 12
  4. 9

Questions & Step-by-Step Solutions

If the vectors A = 2i + 3j and B = 3i + 4j are perpendicular, what is the value of A · B?
  • Step 1: Understand that two vectors are perpendicular if the angle between them is 90 degrees.
  • Step 2: Recall that the dot product of two vectors A and B is given by A · B = |A| |B| cos(θ), where θ is the angle between them.
  • Step 3: Since A and B are perpendicular, the angle θ = 90 degrees.
  • Step 4: The cosine of 90 degrees is 0, so cos(90°) = 0.
  • Step 5: Therefore, A · B = |A| |B| cos(90°) = |A| |B| * 0 = 0.
  • Step 6: Conclude that if A and B are perpendicular, then A · B = 0.
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