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**woollybull** Prove that, if (**c**-**b**).**a** = 0 and (**c**-**a**).**b **= 0, then (**b**-**a**).**c**=0. Show that this can be used to prove the following geometrical results.

(a) The lines through the vertices of a triangle ABC perpendicular to the opposite sides meet in a point.

I can do the first part by using the distributive rule and communitative rule for scalar products.

But part (a) took a too much effort for what I think is meant to be a simple question. I showed that the lines through the vertices can be expressed in the one vector, therefore they must meet in a point. I used the fact that their dot product is zero. It took a hell of a lot of tedious algebra and I'm not even sure that its right. I'd appreciate any help.

Thanks.