Vector Problem

Hey guys, having trouble with this vector problem, I've been spending a long time on it now and am getting quite frustrated, any help would be very much appreciated.

If a, b and c are coplanar vectors related by

\lambda\mathbf{a} + \mu\mathbf{b} + \nu\mathbf{c} = \mathbf{0}

where λ, μ and ν are non-zero, show that the condition for the points with position vectors αa, βb and γc to be colinear is

\frac{\lambda}{\alpha} + \frac{\mu}{\beta} + \frac{\nu}{\gamma} = 0

I've tried various stuff like using the fact they are collinear to express γc in terms of a and b and subbbing them in, but keep getting into big messes. I'm not really just what sort of direction I should be heading in, any hints would be great.

Thanks in advance!

Reply 1

DFranklin

Have a look at http://www.thestudentroom.co.uk/showthread.php?p=10083696&highlight=vector+coplanar+colinear#post10083696

My solution seemed a bit over-complicated, but I don't think anyone came up with anything better.

Where's the question from, by the way?

Reply 2

Nichrome

Thanks alot for the link, should have searched the forum before posting myself really, stupid of me! :redface:

The question is from the Riley, Hobson, Bence book, Mathematical Methods for Physicists and Engineers.

Reply 3

DFranklin

Nichrome

Thanks alot for the link, should have searched the forum before posting myself really, stupid of me! :redface:

I wouldn't have thought to in your position. Just odd that someone else posted it just a week ago, so I recognized it.

The question is from the Riley, Hobson, Bence book, Mathematical Methods for Physicists and Engineers.

OK. Felt more like a university question than A-level.

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