Question

When two vectors have a 0 dot product, which of the following is true?

a. The vectors are orthogonal.
b. The vectors are parallel.
c. The vectors have equal magnitudes.
d. None of the above

Answer 1

The statement that when two vectors have a 0 dot product, they are orthogonal, is true because a 0 dot product indicates that the vectors are at a 90-degree angle to each other.

Step-by-step explanation:

When two vectors have a 0 dot product, it indicates that the two vectors are orthogonal to each other. The dot product, also known as scalar product, of two vectors involves multiplying their magnitudes and the cosine of the angle between them. For the result to be zero, the cosine of the angle must be zero, which only occurs when the angle is 90 degrees, meaning the vectors are perpendicular. Therefore, the vectors do not need to be parallel or have equal magnitudes; they must be at right angles to one another.