Question

What does a cross product of $0$ mean?

Answer 1

Cross Product of vectors:

Cross product means vector product and it is represented as $\overrightarrow{\mathbf{A}}\mathbf{}\mathbf{\times }\overrightarrow{\mathbf{B}}\mathbf{=}\mathit{A}\mathit{B}\mathbf{sin}\mathit{\theta }\hat{\mathbf{\eta }}$, where $\overrightarrow{A,}\overrightarrow{B}$are vectors and $A,B$ represent magnitude of vectors, $\hat{\eta }$ is unit vector and and $\theta$ is angle between the vectors.

If the cross product of two vectors is zero then

1. The vectors are parallel to each other or the angle between them is an even multiple of $90°$.
2. Either one of the vectors or both the vectors are zero vectors.

Hence, meaning of cross product is zero defined.