How to calculate the parallelism of space vectors?

The parallel judgment of space vectors can be determined by whether their direction vectors are proportional.

Judging whether two space vectors are parallel, we can compare whether their direction vectors are proportional. If the direction vectors of two vectors are directly proportional, that is, the ratio between each of their components is equal, then the two vectors are parallel. The specific calculation method is as follows: There are two vectors A and B, and their direction vectors are (Ax, Ay, Az) and (Bx, By, Bz) respectively. If there is a non-zero real number k such that Ax/k = Bx, Ay/k = By, Az/k = Bz, then vector a and vector b are parallel.