# Vector Problem

1. Dec 15, 2009

### thepopasmurf

1. The problem statement, all variables and given/known data
The greek letters look like they're superscripted, they're not supposed to be.
a, b, c are vectors

given that
$$\lambda$$a + $$\mu$$ b + $$\nu$$c=0

show that the points $$\alpha$$a, $$\beta$$b and $$\gamma$$c are collinear if

$$\lambda$$/$$\alpha$$ + $$\mu$$/$$\beta$$ + $$\nu$$/$$\gamma$$ = 0

2. Relevant equations

There are a lot of potentially relevant equations. Most important:
lines are collinear if a = xb

3. The attempt at a solution
My attempt is really long so I won't post it here, I'll just outline my method.

I found the line between $$\alpha$$a and $$\beta$$b and said it was equal to x times the line between $$\beta$$b and $$\gamma$$c.

I also found a in terms of b and c from
$$\lambda$$a +$$\mu$$b + $$\nu$$c=0

and subbed it into the former equation. However I got stuck because I had an x that I couldn't get rid of.

2. Dec 16, 2009

### tiny-tim

Hi thepopasmurf!
Nooo … most important is the cross product equation, (p - q) x (q - r) = 0.

3. Dec 16, 2009

### thepopasmurf

Thank you, solved it. I forgot about that one