Intersection point of 2 vectors in R3

Hi everyone,

i'm not quite sure where this thread should go but here i go.

I have 2 vectors

Here are the 2 points for vector 1 (in R3)

V1 :

Here is the symetric equation of vector 2

V2 :

My parametric equations for those 2 vectors should be :

V1: [LaTeX ERROR:
Compile failed]

V2: [LaTeX ERROR:
Compile failed]

My problem is that I need to find the unknown a in order for my 2 vector to have one intersection point. I'm missing something but i cannot pinpoint what... and this is driving me nuts. Finding V1 // V2 is easy as well as V1 perpendicular to V2 but i'm missing something obvious.

any help would be appreciated.