Question

If the dot product of two vectors vanishes, what can you say about their directions?

a) Parallel
b) Perpendicular
c) Opposite
d) Cannot be determined

Answer 1

The dot product of two vectors is zero when the vectors are perpendicular to each other, meaning they form a 90° angle.

Step-by-step explanation:

If the dot product of two vectors vanishes, this means that the vectors are perpendicular to each other. It implies that the angle between them is 90°.

This arises from the definition of the dot product, which is •A •B = |A| |B| cos(θ), where θ is the angle between the vectors A and B.

If this product equals zero, it must be that cos(θ) equals zero, which happens when θ is 90° or π/2 radians. Therefore, the correct answer is b) They are perpendicular, forming a 90° angle between each other.