1. ## Parallel Vectors

Hi,

What does it exactly mean when vectors are parallel? There must be something that I do not understand because in the following question:

"The line L is parallel to the z - axis . The point P has a position vector (8,1,0) and lies on L .

Write down the equation of L in the for r = a +tb."

I understand that a is the position vector and b is the direction, however no direction is directly stated. Apparently the answer for b is (0,0,1). So if the vector is parallel to the z axis why is the last number 1?

I understand that in 3D vectors, it is in the form (x,y,z).

$<0,0,1>,~<0,0,-\pi>,~<0,0,12>$ are three parallel vectors.
It is custom to use these three as a basis for $\mathcal{R}^3$: $<1,0,0>,~<0,1,0>,~<0,0,1>$