26.5 Parallel Vectors

If two non-zero vectors \(\underline {a}\) and \(\underline {b}\) are parallel then one is a scalar multiple of the other, \(\underline {a}=\lambda \underline {b}\) for some \(\lambda \neq 0\). The converse holds too, so this is the standard test for parallelism — and, in geometry problems, the standard way to prove three points collinear.