# Vector geometry and trigonometry

1. Sep 13, 2008

### Excelled

A friend needed help with his linear algebra assignment, but after looking at it a long time, I can't say I can help him very much. (Apparently they are working with http://local.wasp.uwa.edu.au/~pbourke/fractals/vankoch_snowflake/".)

1. The problem statement, all variables and given/known data
"Given the points P and Q, derive formulae for A, B and C using vector geometry."
http://bayimg.com/image/makmkaabh.jpg [Broken]

2. Relevant equations
|PA| = |AB| = |AC| = |BC| = |CQ|
(ABC is therefore an equilateral triangle.)

3. The attempt at a solution
PA is easy, of course, since it's just (1/3)(PQ), and PC is just (2/3)(PQ).

But how do you define the vector PB from what's given? (I tried by vector addition, adding a vector PA rotated 60 degrees to PA, but I couldn't make it a comprehensible, general formula.)

Last edited by a moderator: May 3, 2017
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