Collinearity of Points: Solving the Equation

[thepopasmurf]

Homework Statement

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

Homework Equations

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

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.

 

[tiny-tim]

Hi thepopasmurf!

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

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

 

[thepopasmurf]

Thank you, solved it. I forgot about that one