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ceva's theorem vector proof, rigourising

Hiya, in the process of prooving cevas theorem using vectors. i have the basis of a proof but theres a lot of smoke and mirrors which i would like to remove.
so i have taken an origin o. a triangle ABC has position vectors a,b,c. o=xa+yb+zc
then i want to show that where the line oa meets bc at d bd/dc = z/y. so what i am trying to do is prove |od|=-x, then the whole thing will fall. however this is the part where i start to wave my hands.

i basically say let the line bc be the i component and perpendicular to that be the j.

then using a drawing show how the removal of the a causes the vertical components of the points b,c and d to all be equal. obviously there is a more formal way to write this. please help. thank you, :smile:

Dan

Reply 1

DFranklin

It's not at all clear what you're doing, but one observation:

If you have two non-zero, non-parallel vectors p and q, and you know that

\lambda{\bf p} + \mu {\bf q} = 0

, then it is legitimate to deduce that

\lambda = \mu = 0

.

(You probably want to choose p = BC here).

Reply 2

marmeduke

Thank you franklin, that is sort of what i was trying to express, but was just going round the houses with words because i couldnt formalise it with maths. :smile: