How are you drawing the vectors? If you are using line() you could use the origin for the first three coordinates, no translations needed.

For example I need a vector starting from (0,0) and end to (100,100) and  another from (200,200) to (400,400). Also I need to use the heading() function to calculate the angle of rotation.

Thanks a lot. I actually have a thought to connect cloud points with vectors in pairs in order to understand if there are a part of a plane by calculate there heading, i.e if the angle is close to 0, is a plane. I did some test but with no luck till now....

I dont know exatly what you mean but what i do know is that there is
1 always a plane through three given points
2 always a plane through one point and one vector

Getting that plane using angle between is not the easiest method i think. There are a lot of math websites that show you ways to calculate.

If you mean to find out if two lines are in the same plane you have to check 2 things:
are the lines (vectors) paralel (just normalize them and check if the normalised vectors are the same or inverse)
do the lines intersect, http://processingjs.org/learning/custom/intersect/  a processing script containing that code

if one of these conditions is met then the vectors are in the same plane