Collinear vector. Properties

Theorem

If there are two non-zero collinear vectors, then there exists a number λ such that



Evidence.

Let a and b be equally directed.



- These are vectors that are equally directed and have the same absolute value | b |. So they are equal:



When vectors a and b are oppositely directed in the same way, we conclude that



The theorem is proved.

Theorem

Any vector with can be represented as