In senior one mathematics, vectors with the same or opposite directions are parallel vectors. Why is this sentence wrong? The answer is that it should be a non-zero vector with the same or opposite direction. Parallel vector (also called * * * line vector): Non-zero vectors A and B with the same or opposite directions are called parallel vectors and recorded as A ∨ B.

This is the definition in the book, please remember.

There is nothing wrong with a zero vector being a parallel vector of any vector.

But first look at the definition of zero vector. The norm of zero vector is zero, and the direction can be arbitrary. It means that it has countless directions, and any vector always has a zero vector parallel or opposite to its direction, so the zero vector becomes a parallel vector of any vector, so it is meaningless for us to discuss the zero vector. It is stipulated in the book that it is meaningful to discuss the parallelism of non-zero vectors for unity.

It is a special case that the zero vector is an equal vector, so it is good to record it separately. There is no need to be so serious, and other related knowledge is also needed. If it is * * *, it must be special.