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If the angle between two vectors A and B is 90 degrees, what is the value of A ·

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Question: If the angle between two vectors A and B is 90 degrees, what is the value of A · B?

Options:

  1. 1
  2. 0
  3. undefined
  4. 1/2

Correct Answer: 0

Solution: 

If the angle is 90 degrees, A · B = |A||B|cos(90) = 0.

If the angle between two vectors A and B is 90 degrees, what is the value of A ·

Practice Questions

Q1
If the angle between two vectors A and B is 90 degrees, what is the value of A · B?
  1. 1
  2. 0
  3. undefined
  4. 1/2

Questions & Step-by-Step Solutions

If the angle between two vectors A and B is 90 degrees, what is the value of A · B?
  • Step 1: Understand that A · B represents the dot product of vectors A and B.
  • Step 2: Recall the formula for the dot product: A · B = |A||B|cos(θ), where θ is the angle between the two vectors.
  • Step 3: Identify that the angle θ in this case is 90 degrees.
  • Step 4: Know that cos(90 degrees) equals 0.
  • Step 5: Substitute the angle into the formula: A · B = |A||B|cos(90) = |A||B| * 0.
  • Step 6: Since anything multiplied by 0 is 0, conclude that A · B = 0.
  • Dot Product of Vectors – The dot product of two vectors A and B is calculated as A · B = |A||B|cos(θ), where θ is the angle between them.
  • Orthogonal Vectors – Vectors are orthogonal (perpendicular) when the angle between them is 90 degrees, resulting in a dot product of zero.
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