Vector Triple Product: Are a & c Parallel or Collinear?

[debjit625]

Hi all got a confusion
In many books I saw , authors used a specific statement here is it

a,b,c are vectors and axb is (" a cross b")
In general
(axb)xc ≠ ax(bxc)
but if
(axb)xc = ax(bxc)
solving it we get
bx(axc)=0
then it implies
either b is parallel to (axc)
or a and c are collinear.

Now my question is can I say a and c are parallel rather co linear ,my confusion arise as all books I referred they all say its co linear.

Now I think in general a and c doesn't have to lie in a same line to get the specific definition of co linearity ,
but I am not sure.

Thanks

 

[BvU]

In 3D we represent a vector with three numbers (x,y,z)
All vectors 'start' in (0,0,0), so if they are parallel they are also colinear (one is a multiple of the other).