English isn't my native language.
I'm learning vector, and i'm having a question.
I know that term 'parallel' is used to show relationship between (two lines) or (two vectors) or (two planes) or (one line and one plane).
Yes, many math books 'define' 'parallel' in these case.
But many math books don't 'define' what is parallel between (one vector and one line).
And they used term 'parallel' between (one vector and one line).
What exactly 'parallel' means between one vector and one line??
Best Answer
Here's a reasonable definition:
A line $\mathbf r=\mathbf p+\lambda\mathbf u$ and a vector $\mathbf v$ are parallel to each other (alternatively: collinear) if there exists some real $k$ such that $\mathbf v=k\mathbf u.$
(In particular, the zero vector is parallel to every line.)