Any ideas how to do this vector problem that a friend asked me about.

The vertices A,B and C of a triangle have non-coplanar position vectors a,b and c relative to an origin O. The points D,E lie on Ab, AC such that AD:DB = 1:2 and AE:EC = 1:2.

The lines BE and CD intersect at the point F. Find the position Vector of F.

Question

Any ideas how to do this vector problem that a friend   asked me about.

The vertices  A,B and C of a triangle have  non-coplanar position vectors  a,b and c relative to an origin O. The points D,E lie on Ab, AC such that AD:DB = 1:2 and AE:EC = 1:2.

The lines BE and CD intersect at the point F. Find the position Vector of F.

cwrw238 · Answer

I can find the PV's of  points E and D ( in terms of a,b and c) as the ratios are given.

but i would imagine  we need to find the position of F on the lines BE and CD.
- that where I'm stuck

cwrw238 · Answer

maybe it involves some item of elementary geometry which i've completely forgotten.....

cwrw238 · Answer

lol -  i may have score of 99 but I'm pretty well stuck on this one...

cwrw238 · Answer

thats a typo - it should be AB

dan815 · Answer

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