i think this is simple, but it still confuses me at times

say i have 2 position vectors:

b= 2i - 3j

c= 3i - 2j + sqrt(2)k

i am asked to give the equation of the line going through these 2 points

i know this equation is given by r=a+ λb

whereais the position vector of a point on the line

(in this case it can beborc)

andbis the Direction Vector of the line, and this can be calculated easily by working out (c-b),

BUT

can the direction Vector also be calculated by working out (b-c)??

Because in doing so the answer will be completely different, but i think that it would still qualify as an equation of a line passing through pointsbandcno?

just wanted to clarify this, thanks in advance for any assistance