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

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

Options:

Correct Answer: 0

Solution:

A · B = |A||B|cos(90°) = |A||B| * 0 = 0.

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

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

Step 1: Understand that A · B represents the dot product of two vectors A and B.
Step 2: Recall that the formula for the dot product is A · B = |A||B|cos(θ), where θ is the angle between the two vectors.
Step 3: In this case, the angle θ is given as 90 degrees.
Step 4: Know that the cosine of 90 degrees is 0 (cos(90°) = 0).
Step 5: Substitute the angle into the dot product formula: A · B = |A||B|cos(90°).
Step 6: This simplifies to A · B = |A||B| * 0.
Step 7: Since anything multiplied by 0 is 0, we 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 the vectors.
Angle Between Vectors – When the angle between two vectors is 90 degrees, they are orthogonal, resulting in a dot product of zero.