1. ## Vector Equations

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

where a is the position vector of a point on the line
(in this case it can be b or c)

and b is 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 points b and c no?

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

2. Yes you can because b-c and c-b are both direction vectors of the line

The answer will not be so different : it is a matter of changing $\lambda$ in $-\lambda$

3. i assumed as much..

still, how do you decide when to switch λ with -λ in the equation?

i mean how do you decide which Direction Vector requires you to do so (b-c) or (c-b)?

thanks again

4. You can write r = a + k(b-c) or r = a + k'(c-b)
It does not matter
The relationship between k and k' is k=-k'

You can choose any direction vector to write r